Dong, Hongjie

Compute Distance To:
 Author ID: dong.hongjie Published as: Dong, Hongjie; Dong, H. Homepage: http://www.dam.brown.edu/people/hdong External Links: MGP · ORCID · Google Scholar · Math-Net.Ru · dblp
 Documents Indexed: 120 Publications since 2005 Co-Authors: 34 Co-Authors with 100 Joint Publications 1,310 Co-Co-Authors
all top 5

Co-Authors

 16 single-authored 24 Kim, Doyoon 15 Kim, Seick 9 Krylov, Nicolaĭ Vladimirovich 8 Li, Dong 7 Choi, Jongkeun 7 Zhang, Hong 6 Li, Zongyuan 5 Du, Dapeng 4 Phan, Tuoc Van 3 Cho, Sungwon 3 Xu, Longjuan 2 Escauriaza Zubiria, Luis 2 Gallarati, Chiara 2 Gu, Xumin 2 Pan, Xinghong 2 Pavlović, Nataša 2 Wang, Kunrui 1 Ammari, Habib M. 1 Bulut, Aynur 1 Gao, Yuan 1 Jin, Tianling 1 Kang, Hyeonbae 1 Lee, Jihoon 1 Li, Xu 1 Peng, Fa 1 Safonov, Mikhail V. 1 Staubach, Wolfgang 1 Strain, Robert M. 1 Xiong, Jingang 1 Yang, Tong 1 Zhang, Yi Ru-Ya 1 Zhong, Mingying 1 Zhou, Yuan 1 Zhu, Hanye
all top 5

Serials

 10 Journal of Functional Analysis 9 Calculus of Variations and Partial Differential Equations 8 Transactions of the American Mathematical Society 8 SIAM Journal on Mathematical Analysis 8 Discrete and Continuous Dynamical Systems 7 IMRN. International Mathematics Research Notices 7 Communications in Partial Differential Equations 6 Archive for Rational Mechanics and Analysis 6 Advances in Mathematics 5 Communications in Mathematical Physics 4 Indiana University Mathematics Journal 4 Journal of Differential Equations 4 Proceedings of the American Mathematical Society 4 Journal of Mathematical Fluid Mechanics 3 St. Petersburg Mathematical Journal 2 Applied Mathematics and Optimization 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Potential Analysis 2 Dynamics of Partial Differential Equations 1 Communications on Pure and Applied Mathematics 1 The Annals of Probability 1 Mathematische Annalen 1 Bulletin of the Korean Mathematical Society 1 Revista Matemática Iberoamericana 1 Electronic Journal of Differential Equations (EJDE) 1 Methods and Applications of Analysis 1 Advances in Computational Mathematics 1 Journal of Evolution Equations 1 Communications on Pure and Applied Analysis 1 Communications in Mathematical Sciences 1 Analysis in Theory and Applications 1 Analysis & PDE 1 Advances in Applied Mathematics and Mechanics 1 Bulletin of Mathematical Sciences 1 Annals of Applied Mathematics
all top 5

Fields

 116 Partial differential equations (35-XX) 25 Fluid mechanics (76-XX) 7 Geophysics (86-XX) 6 Mechanics of deformable solids (74-XX) 4 Probability theory and stochastic processes (60-XX) 4 Numerical analysis (65-XX) 4 Statistical mechanics, structure of matter (82-XX) 2 Real functions (26-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral equations (45-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Operator theory (47-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Optics, electromagnetic theory (78-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX)

Citations contained in zbMATH Open

97 Publications have been cited 1,177 times in 674 Documents Cited by Year
Elliptic equations in divergence form with partially BMO coefficients. Zbl 1206.35249
Dong, Hongjie; Kim, Doyoon
2010
On the $$L_p$$-solvability of higher-order parabolic and elliptic systems with BMO coefficients. Zbl 1228.35113
Dong, Hongjie; Kim, Doyoon
2011
Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains. Zbl 1231.35093
Dong, Hongjie; Kim, Doyoon
2011
Parabolic and elliptic systems in divergence form with variably partially BMO coefficients. Zbl 1230.35045
Dong, Hongjie; Kim, Doyoon
2011
Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space. Zbl 1141.35436
Dong, Hongjie; Du, Dapeng
2008
Schauder estimates for a class of non-local elliptic equations. Zbl 1263.45008
Dong, Hongjie; Kim, Doyoon
2013
Gradient estimates for parabolic and elliptic systems from linear laminates. Zbl 1258.35040
Dong, Hongjie
2012
On $$L_p$$-estimates for elliptic and parabolic equations with $$A_p$$ weights. Zbl 1427.35305
Dong, Hongjie; Kim, Doyoon
2018
On $$L_p$$-estimates for a class of non-local elliptic equations. Zbl 1232.35182
Dong, Hongjie; Kim, Doyoon
2012
Finite time singularities and global well-posedness for fractal Burgers equations. Zbl 1166.35030
Dong, Hongjie; Du, Dapeng; Li, Dong
2009
Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness. Zbl 1186.35158
Dong, Hongjie
2010
$$L_p$$ solvability of divergence type parabolic and elliptic systems with partially BMO coefficients. Zbl 1216.35160
Dong, Hongjie; Kim, Doyoon
2011
Well-posedness for a transport equation with nonlocal velocity. Zbl 1170.35004
Dong, Hongjie
2008
A regularity criterion for the dissipative quasi-geostrophic equations. Zbl 1176.35133
Dong, Hongjie; Pavlović, Nataša
2009
Parabolic and elliptic systems with VMO coefficients. Zbl 1197.35066
Dong, Hongjie; Kim, Doyoon
2009
Green’s matrices of second order elliptic systems with measurable coefficients in two dimensional domains. Zbl 1173.35050
Dong, Hongjie; Kim, Seick
2009
On $$C^1$$, $$C^2$$, and weak type-$$(1,1)$$ estimates for linear elliptic operators. II. Zbl 1406.35071
Dong, Hongjie; Escauriaza, Luis; Kim, Seick
2018
Spatial analyticity of the solutions to the subcritical dissipative quasi-geostrophic equations. Zbl 1157.35456
Dong, Hongjie; Li, Dong
2008
Optimal local smoothing and analyticity rate estimates for the generalized Navier-Stokes equations. Zbl 1173.35626
Dong, Hongjie; Li, Dong
2009
The rate of convergence of finite-difference approximations for parabolic bellman equations with Lipschitz coefficients in cylindrical domains. Zbl 1127.65068
Dong, Hongjie; Krylov, Nicolai V.
2007
Global regularity of weak solutions to quasilinear elliptic and parabolic equations with controlled growth. Zbl 1233.35059
Dong, Hongjie; Kim, Doyoon
2011
Solvability of parabolic equations in divergence form with partially BMO coefficients. Zbl 1191.35145
Dong, Hongjie
2010
On the 2D critical and supercritical dissipative quasi-geostrophic equation in Besov spaces. Zbl 1193.35151
Dong, Hongjie; Li, Dong
2010
The Navier-Stokes equations in the critical Lebesgue space. Zbl 1216.35085
Dong, Hongjie; Du, Dapeng
2009
Partial regularity of solutions to the four-dimensional Navier-Stokes equations at the first blow-up time. Zbl 1156.35442
Dong, Hongjie; Du, Dapeng
2007
Weighted $$L_{q}$$-estimates for stationary Stokes system with partially BMO coefficients. Zbl 1479.35159
Dong, Hongjie; Kim, Doyoon
2018
On $$C^{1}$$, $$C^{2}$$, and weak type-$$(1,1)$$ estimates for linear elliptic operators. Zbl 1373.35117
Dong, Hongjie; Kim, Seick
2017
$$L_{p}$$-estimates for time fractional parabolic equations with coefficients measurable in time. Zbl 1447.35352
Dong, Hongjie; Kim, Doyoon
2019
Regularity criteria for the dissipative quasi-geostrophic equations in Hölder spaces. Zbl 1185.35187
Dong, Hongjie; Pavlović, Nataša
2009
On the Green’s matrices of strongly parabolic systems of second order. Zbl 1170.35005
Cho, Sungwon; Dong, Hongjie; Kim, Seick
2008
Second-order elliptic and parabolic equations with $$B(\mathbb R^2, \mathrm{VMO})$$ coefficients. Zbl 1207.35174
Dong, Hongjie; Krylov, N. V.
2010
On the local smoothness of solutions of the Navier-Stokes equations. Zbl 1128.35081
Dong, Hongjie; Du, Dapeng
2007
On partial regularity of steady-state solutions to the 6D Navier-Stokes equations. Zbl 1286.35193
Dong, Hongjie; Strain, Robert M.
2012
Elliptic and parabolic equations with measurable coefficients in weighted Sobolev spaces. Zbl 1373.35114
Dong, Hongjie; Kim, Doyoon
2015
Finite time singularities for a class of generalized surface quasi-geostrophic equations. Zbl 1143.35084
Dong, Hongjie; Li, Dong
2008
Conormal derivative problems for stationary Stokes system in Sobolev spaces. Zbl 1393.35259
Choi, Jongkeun; Dong, Hongjie; Kim, Doyoon
2018
On uniqueness of boundary blow-up solutions of a class of nonlinear elliptic equations. Zbl 1153.35039
Dong, Hongjie; Kim, Seick; Safonov, Mikhail
2008
Partial Schauder estimates for second-order elliptic and parabolic equations. Zbl 1221.35078
Dong, Hongjie; Kim, Seick
2011
The aggregation equation with power-law kernels: ill-posedness, mass concentration and similarity solutions. Zbl 1222.35205
Dong, Hongjie
2011
On a one-dimensional $$\alpha$$-patch model with nonlocal drift and fractional dissipation. Zbl 1302.35334
Dong, Hongjie; Li, Dong
2014
Rate of convergence of finite-difference approximations for degenerate linear parabolic equations with $$C^1$$ and $$C^2$$ coefficients. Zbl 1085.65087
Dong, Hongjie; Krylov, Nicolai V.
2005
Global estimates for Green’s matrix of second order parabolic systems with application to elliptic systems in two dimensional domains. Zbl 1242.35067
Cho, Sungwon; Dong, Hongjie; Kim, Seick
2012
Solvability of second-order equations with hierarchically partially BMO coefficients. Zbl 1242.35132
Dong, Hongjie
2012
Optimal estimates for the conductivity problem by Green’s function method. Zbl 1412.35082
Dong, Hongjie; Li, Haigang
2019
Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces. Zbl 1418.35211
Dong, Hongjie; Krylov, N. V.
2019
Partial regularity of solutions to the four-dimensional Navier-Stokes equations. Zbl 1294.35060
Dong, Hongjie; Gu, Xumin
2014
On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains. Zbl 1278.35133
Dong, Hongjie; Krylov, N. V.; Li, Xu
2013
The conormal derivative problem for higher order elliptic systems with irregular coefficients. Zbl 1317.35068
Dong, Hongjie; Kim, Doyoon
2012
Boundary partial regularity for the high dimensional Navier-Stokes equations. Zbl 1300.35070
Dong, Hongjie; Gu, Xumin
2014
On an elliptic equation arising from composite materials. Zbl 1351.35041
Dong, Hongjie; Zhang, Hong
2016
Dini and Schauder estimates for nonlocal fully nonlinear parabolic equations with drifts. Zbl 1392.35048
Dong, Hongjie; Jin, Tianling; Zhang, Hong
2018
Schauder estimates for higher-order parabolic systems with time irregular coefficients. Zbl 1323.35073
Dong, Hongjie; Zhang, Hong
2015
Boundary gradient estimates for parabolic and elliptic systems from linear laminates. Zbl 1329.35140
Dong, Hongjie; Xiong, Jingang
2015
Conormal problem of higher-order parabolic systems with time irregular coefficients. Zbl 1334.35090
Dong, Hongjie; Zhang, Hong
2016
On the rate of convergence of finite-difference approximations for Bellman equations with constant coefficients. Zbl 1136.49312
Dong, Hongjie; Krylov, N. V.
2006
Unique continuation for the Schrödinger equation with gradient vector potentials. Zbl 1119.35083
Dong, Hongjie; Staubach, Wolfgang
2007
On time-inhomogeneous controlled diffusion processes in domains. Zbl 1127.93062
Dong, Hongjie; Krylov, N. V.
2007
On conormal and oblique derivative problem for elliptic equations with Dini mean oscillation coefficients. Zbl 1459.35119
Dong, Hongjie; Lee, Jihoon; Kim, Seick
2020
On the impossibility of $$W_p^2$$ estimates for elliptic equations with piecewise constant coefficients. Zbl 1302.35143
Dong, Hongjie; Kim, Doyoon
2014
Green functions of conormal derivative problems for stationary Stokes system. Zbl 1404.35348
Choi, Jongkeun; Dong, Hongjie; Kim, Doyoon
2018
$$L_p$$-estimates for time fractional parabolic equations in divergence form with measurable coefficients. Zbl 1427.35316
Dong, Hongjie; Kim, Doyoon
2020
On the existence of smooth solutions for fully nonlinear parabolic equations with measurable “coefficients” without convexity assumptions. Zbl 1479.35526
Dong, Hongjie; Krylov, N. V.
2013
Hessian equations with elementary symmetric functions. Zbl 1237.35051
Dong, Hongjie
2006
Fundamental solutions for second-order parabolic systems with drift terms. Zbl 1391.35007
Dong, Hongjie; Kim, Seick
2018
Parabolic equations with variably partially VMO coefficients. Zbl 1252.35149
Dong, H.
2012
On similarity solutions to the multidimensional aggregation equation. Zbl 1235.35064
Dong, Hongjie
2011
Gradient estimates for divergence form elliptic systems arising from composite material. Zbl 1429.35075
Dong, Hongjie; Xu, Longjuan
2019
Partial Schauder estimates for second-order elliptic and parabolic equations: a revisit. Zbl 1428.35059
Dong, Hongjie; Kim, Seick
2019
On a multi-dimensional transport equation with nonlocal velocity. Zbl 1296.35210
Dong, Hongjie
2014
Time analyticity for the heat equation and Navier-Stokes equations. Zbl 1448.35270
Dong, Hongjie; Zhang, Qi S.
2020
Regularity for parabolic equations with singular or degenerate coefficients. Zbl 1459.35054
Dong, Hongjie; Phan, Tuoc
2021
Classical solutions of oblique derivative problem in nonsmooth domains with mean Dini coefficients. Zbl 1444.35043
Dong, Hongjie; Li, Zongyuan
2020
Neumann problem for non-divergence elliptic and parabolic equations with $$\mathrm{BMO}_x$$ coefficients in weighted Sobolev spaces. Zbl 1351.35039
Kim, Doyoon; Dong, Hongjie; Zhang, Hong
2016
Higher-order elliptic and parabolic equations with VMO assumptions and general boundary conditions. Zbl 1387.35079
Dong, Hongjie; Gallarati, Chiara
2018
Gradient estimates for Stokes systems in domains. Zbl 1404.35162
Choi, Jongkeun; Dong, Hongjie
2019
On Schauder estimates for a class of nonlocal fully nonlinear parabolic equations. Zbl 1406.35156
Dong, Hongjie; Zhang, Hong
2019
On elliptic equations in a half space or in convex wedges with irregular coefficients. Zbl 1281.35018
Dong, Hongjie
2013
Existence and uniqueness of bounded stable solutions to the Peierls-Nabarro model for curved dislocations. Zbl 1462.35437
Dong, Hongjie; Gao, Yuan
2021
Weighted mixed-norm $$L_p$$-estimates for elliptic and parabolic equations in non-divergence form with singular coefficients. Zbl 1467.35066
Dong, Hongjie; Phan, Tuoc
2021
Optimal regularity for a Dirichlet-conormal problem in Reifenberg flat domain. Zbl 1471.35114
Choi, Jongkeun; Dong, Hongjie; Li, Zongyuan
2021
Mixed-norm $$L_p$$-estimates for non-stationary Stokes systems with singular VMO coefficients and applications. Zbl 07297753
Dong, Hongjie; Phan, Tuoc
2021
Hessian estimates for equations involving $$p$$-Laplacian via a fundamental inequality. Zbl 1442.35195
Dong, Hongjie; Peng, Fa; Zhang, Yi Ru-Ya; Zhou, Yuan
2020
Parabolic equations in simple convex polytopes with time irregular coefficients. Zbl 1304.35320
Dong, Hongjie; Kim, Doyoon
2014
Dini estimates for nonlocal fully nonlinear elliptic equations. Zbl 1394.35061
Dong, Hongjie; Zhang, Hong
2018
Green’s functions for parabolic systems of second order in time-varying domains. Zbl 1284.35207
Dong, Hongjie; Kim, Seick
2014
Boundary $$\varepsilon$$-regularity criteria for the three-dimensional Navier-Stokes equations. Zbl 1435.35276
Dong, Hongjie; Wang, Kunrui
2020
Recent progress in the $${L_p}$$ theory for elliptic and parabolic equations with discontinuous coefficients. Zbl 1474.35243
Dong, Hongjie
2020
The Dirichlet-conormal problem with homogeneous and inhomogeneous boundary conditions. Zbl 1467.35130
Dong, Hongjie; Li, Zongyuan
2021
$$L_q$$-estimates for stationary Stokes system with coefficients measurable in one direction. Zbl 1467.35065
Dong, Hongjie; Kim, Doyoon
2019
On a generalized maximum principle for a transport-diffusion model with $$\log$$-modulated fractional dissipation. Zbl 1304.35538
Dong, Hongjie; Li, Dong
2014
On an elliptic equation arising from photo-acoustic imaging in inhomogeneous media. Zbl 1339.35310
Ammari, Habib; Dong, Hongjie; Kang, Hyeonbae; Kim, Seick
2015
Boundary value problems for parabolic operators in a time-varying domain. Zbl 1327.35135
Cho, Sungwon; Dong, Hongjie; Kim, Doyoon
2015
Global $$\dot H^1 \cap \dot H^{-1}$$ solutions to a logarithmically regularized $$2D$$ Euler equation. Zbl 1320.35268
Dong, Hongjie; Li, Dong
2015
Gradient estimates for Stokes systems with Dini mean oscillation coefficients. Zbl 1442.35329
Choi, Jongkeun; Dong, Hongjie
2019
Hessian estimates for non-divergence form elliptic equations arising from composite materials. Zbl 1472.35120
Dong, Hongjie; Xu, Longjuan
2021
The conormal and Robin boundary value problems in nonsmooth domains satisfying a measure condition. Zbl 1473.35160
Dong, Hongjie; Li, Zongyuan
2021
Time analyticity for inhomogeneous parabolic equations and the Navier-Stokes equations in the half space. Zbl 1447.35089
Dong, Hongjie; Pan, Xinghong
2020
Regularity for parabolic equations with singular or degenerate coefficients. Zbl 1459.35054
Dong, Hongjie; Phan, Tuoc
2021
Existence and uniqueness of bounded stable solutions to the Peierls-Nabarro model for curved dislocations. Zbl 1462.35437
Dong, Hongjie; Gao, Yuan
2021
Weighted mixed-norm $$L_p$$-estimates for elliptic and parabolic equations in non-divergence form with singular coefficients. Zbl 1467.35066
Dong, Hongjie; Phan, Tuoc
2021
Optimal regularity for a Dirichlet-conormal problem in Reifenberg flat domain. Zbl 1471.35114
Choi, Jongkeun; Dong, Hongjie; Li, Zongyuan
2021
Mixed-norm $$L_p$$-estimates for non-stationary Stokes systems with singular VMO coefficients and applications. Zbl 07297753
Dong, Hongjie; Phan, Tuoc
2021
The Dirichlet-conormal problem with homogeneous and inhomogeneous boundary conditions. Zbl 1467.35130
Dong, Hongjie; Li, Zongyuan
2021
Hessian estimates for non-divergence form elliptic equations arising from composite materials. Zbl 1472.35120
Dong, Hongjie; Xu, Longjuan
2021
The conormal and Robin boundary value problems in nonsmooth domains satisfying a measure condition. Zbl 1473.35160
Dong, Hongjie; Li, Zongyuan
2021
On conormal and oblique derivative problem for elliptic equations with Dini mean oscillation coefficients. Zbl 1459.35119
Dong, Hongjie; Lee, Jihoon; Kim, Seick
2020
$$L_p$$-estimates for time fractional parabolic equations in divergence form with measurable coefficients. Zbl 1427.35316
Dong, Hongjie; Kim, Doyoon
2020
Time analyticity for the heat equation and Navier-Stokes equations. Zbl 1448.35270
Dong, Hongjie; Zhang, Qi S.
2020
Classical solutions of oblique derivative problem in nonsmooth domains with mean Dini coefficients. Zbl 1444.35043
Dong, Hongjie; Li, Zongyuan
2020
Hessian estimates for equations involving $$p$$-Laplacian via a fundamental inequality. Zbl 1442.35195
Dong, Hongjie; Peng, Fa; Zhang, Yi Ru-Ya; Zhou, Yuan
2020
Boundary $$\varepsilon$$-regularity criteria for the three-dimensional Navier-Stokes equations. Zbl 1435.35276
Dong, Hongjie; Wang, Kunrui
2020
Recent progress in the $${L_p}$$ theory for elliptic and parabolic equations with discontinuous coefficients. Zbl 1474.35243
Dong, Hongjie
2020
Time analyticity for inhomogeneous parabolic equations and the Navier-Stokes equations in the half space. Zbl 1447.35089
Dong, Hongjie; Pan, Xinghong
2020
$$L_{p}$$-estimates for time fractional parabolic equations with coefficients measurable in time. Zbl 1447.35352
Dong, Hongjie; Kim, Doyoon
2019
Optimal estimates for the conductivity problem by Green’s function method. Zbl 1412.35082
Dong, Hongjie; Li, Haigang
2019
Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces. Zbl 1418.35211
Dong, Hongjie; Krylov, N. V.
2019
Gradient estimates for divergence form elliptic systems arising from composite material. Zbl 1429.35075
Dong, Hongjie; Xu, Longjuan
2019
Partial Schauder estimates for second-order elliptic and parabolic equations: a revisit. Zbl 1428.35059
Dong, Hongjie; Kim, Seick
2019
Gradient estimates for Stokes systems in domains. Zbl 1404.35162
Choi, Jongkeun; Dong, Hongjie
2019
On Schauder estimates for a class of nonlocal fully nonlinear parabolic equations. Zbl 1406.35156
Dong, Hongjie; Zhang, Hong
2019
$$L_q$$-estimates for stationary Stokes system with coefficients measurable in one direction. Zbl 1467.35065
Dong, Hongjie; Kim, Doyoon
2019
Gradient estimates for Stokes systems with Dini mean oscillation coefficients. Zbl 1442.35329
Choi, Jongkeun; Dong, Hongjie
2019
On $$L_p$$-estimates for elliptic and parabolic equations with $$A_p$$ weights. Zbl 1427.35305
Dong, Hongjie; Kim, Doyoon
2018
On $$C^1$$, $$C^2$$, and weak type-$$(1,1)$$ estimates for linear elliptic operators. II. Zbl 1406.35071
Dong, Hongjie; Escauriaza, Luis; Kim, Seick
2018
Weighted $$L_{q}$$-estimates for stationary Stokes system with partially BMO coefficients. Zbl 1479.35159
Dong, Hongjie; Kim, Doyoon
2018
Conormal derivative problems for stationary Stokes system in Sobolev spaces. Zbl 1393.35259
Choi, Jongkeun; Dong, Hongjie; Kim, Doyoon
2018
Dini and Schauder estimates for nonlocal fully nonlinear parabolic equations with drifts. Zbl 1392.35048
Dong, Hongjie; Jin, Tianling; Zhang, Hong
2018
Green functions of conormal derivative problems for stationary Stokes system. Zbl 1404.35348
Choi, Jongkeun; Dong, Hongjie; Kim, Doyoon
2018
Fundamental solutions for second-order parabolic systems with drift terms. Zbl 1391.35007
Dong, Hongjie; Kim, Seick
2018
Higher-order elliptic and parabolic equations with VMO assumptions and general boundary conditions. Zbl 1387.35079
Dong, Hongjie; Gallarati, Chiara
2018
Dini estimates for nonlocal fully nonlinear elliptic equations. Zbl 1394.35061
Dong, Hongjie; Zhang, Hong
2018
On $$C^{1}$$, $$C^{2}$$, and weak type-$$(1,1)$$ estimates for linear elliptic operators. Zbl 1373.35117
Dong, Hongjie; Kim, Seick
2017
On an elliptic equation arising from composite materials. Zbl 1351.35041
Dong, Hongjie; Zhang, Hong
2016
Conormal problem of higher-order parabolic systems with time irregular coefficients. Zbl 1334.35090
Dong, Hongjie; Zhang, Hong
2016
Neumann problem for non-divergence elliptic and parabolic equations with $$\mathrm{BMO}_x$$ coefficients in weighted Sobolev spaces. Zbl 1351.35039
Kim, Doyoon; Dong, Hongjie; Zhang, Hong
2016
Elliptic and parabolic equations with measurable coefficients in weighted Sobolev spaces. Zbl 1373.35114
Dong, Hongjie; Kim, Doyoon
2015
Schauder estimates for higher-order parabolic systems with time irregular coefficients. Zbl 1323.35073
Dong, Hongjie; Zhang, Hong
2015
Boundary gradient estimates for parabolic and elliptic systems from linear laminates. Zbl 1329.35140
Dong, Hongjie; Xiong, Jingang
2015
On an elliptic equation arising from photo-acoustic imaging in inhomogeneous media. Zbl 1339.35310
Ammari, Habib; Dong, Hongjie; Kang, Hyeonbae; Kim, Seick
2015
Boundary value problems for parabolic operators in a time-varying domain. Zbl 1327.35135
Cho, Sungwon; Dong, Hongjie; Kim, Doyoon
2015
Global $$\dot H^1 \cap \dot H^{-1}$$ solutions to a logarithmically regularized $$2D$$ Euler equation. Zbl 1320.35268
Dong, Hongjie; Li, Dong
2015
On a one-dimensional $$\alpha$$-patch model with nonlocal drift and fractional dissipation. Zbl 1302.35334
Dong, Hongjie; Li, Dong
2014
Partial regularity of solutions to the four-dimensional Navier-Stokes equations. Zbl 1294.35060
Dong, Hongjie; Gu, Xumin
2014
Boundary partial regularity for the high dimensional Navier-Stokes equations. Zbl 1300.35070
Dong, Hongjie; Gu, Xumin
2014
On the impossibility of $$W_p^2$$ estimates for elliptic equations with piecewise constant coefficients. Zbl 1302.35143
Dong, Hongjie; Kim, Doyoon
2014
On a multi-dimensional transport equation with nonlocal velocity. Zbl 1296.35210
Dong, Hongjie
2014
Parabolic equations in simple convex polytopes with time irregular coefficients. Zbl 1304.35320
Dong, Hongjie; Kim, Doyoon
2014
Green’s functions for parabolic systems of second order in time-varying domains. Zbl 1284.35207
Dong, Hongjie; Kim, Seick
2014
On a generalized maximum principle for a transport-diffusion model with $$\log$$-modulated fractional dissipation. Zbl 1304.35538
Dong, Hongjie; Li, Dong
2014
Schauder estimates for a class of non-local elliptic equations. Zbl 1263.45008
Dong, Hongjie; Kim, Doyoon
2013
On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains. Zbl 1278.35133
Dong, Hongjie; Krylov, N. V.; Li, Xu
2013
On the existence of smooth solutions for fully nonlinear parabolic equations with measurable “coefficients” without convexity assumptions. Zbl 1479.35526
Dong, Hongjie; Krylov, N. V.
2013
On elliptic equations in a half space or in convex wedges with irregular coefficients. Zbl 1281.35018
Dong, Hongjie
2013
Gradient estimates for parabolic and elliptic systems from linear laminates. Zbl 1258.35040
Dong, Hongjie
2012
On $$L_p$$-estimates for a class of non-local elliptic equations. Zbl 1232.35182
Dong, Hongjie; Kim, Doyoon
2012
On partial regularity of steady-state solutions to the 6D Navier-Stokes equations. Zbl 1286.35193
Dong, Hongjie; Strain, Robert M.
2012
Global estimates for Green’s matrix of second order parabolic systems with application to elliptic systems in two dimensional domains. Zbl 1242.35067
Cho, Sungwon; Dong, Hongjie; Kim, Seick
2012
Solvability of second-order equations with hierarchically partially BMO coefficients. Zbl 1242.35132
Dong, Hongjie
2012
The conormal derivative problem for higher order elliptic systems with irregular coefficients. Zbl 1317.35068
Dong, Hongjie; Kim, Doyoon
2012
Parabolic equations with variably partially VMO coefficients. Zbl 1252.35149
Dong, H.
2012
On the $$L_p$$-solvability of higher-order parabolic and elliptic systems with BMO coefficients. Zbl 1228.35113
Dong, Hongjie; Kim, Doyoon
2011
Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains. Zbl 1231.35093
Dong, Hongjie; Kim, Doyoon
2011
Parabolic and elliptic systems in divergence form with variably partially BMO coefficients. Zbl 1230.35045
Dong, Hongjie; Kim, Doyoon
2011
$$L_p$$ solvability of divergence type parabolic and elliptic systems with partially BMO coefficients. Zbl 1216.35160
Dong, Hongjie; Kim, Doyoon
2011
Global regularity of weak solutions to quasilinear elliptic and parabolic equations with controlled growth. Zbl 1233.35059
Dong, Hongjie; Kim, Doyoon
2011
Partial Schauder estimates for second-order elliptic and parabolic equations. Zbl 1221.35078
Dong, Hongjie; Kim, Seick
2011
The aggregation equation with power-law kernels: ill-posedness, mass concentration and similarity solutions. Zbl 1222.35205
Dong, Hongjie
2011
On similarity solutions to the multidimensional aggregation equation. Zbl 1235.35064
Dong, Hongjie
2011
Elliptic equations in divergence form with partially BMO coefficients. Zbl 1206.35249
Dong, Hongjie; Kim, Doyoon
2010
Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness. Zbl 1186.35158
Dong, Hongjie
2010
Solvability of parabolic equations in divergence form with partially BMO coefficients. Zbl 1191.35145
Dong, Hongjie
2010
On the 2D critical and supercritical dissipative quasi-geostrophic equation in Besov spaces. Zbl 1193.35151
Dong, Hongjie; Li, Dong
2010
Second-order elliptic and parabolic equations with $$B(\mathbb R^2, \mathrm{VMO})$$ coefficients. Zbl 1207.35174
Dong, Hongjie; Krylov, N. V.
2010
Finite time singularities and global well-posedness for fractal Burgers equations. Zbl 1166.35030
Dong, Hongjie; Du, Dapeng; Li, Dong
2009
A regularity criterion for the dissipative quasi-geostrophic equations. Zbl 1176.35133
Dong, Hongjie; Pavlović, Nataša
2009
Parabolic and elliptic systems with VMO coefficients. Zbl 1197.35066
Dong, Hongjie; Kim, Doyoon
2009
Green’s matrices of second order elliptic systems with measurable coefficients in two dimensional domains. Zbl 1173.35050
Dong, Hongjie; Kim, Seick
2009
Optimal local smoothing and analyticity rate estimates for the generalized Navier-Stokes equations. Zbl 1173.35626
Dong, Hongjie; Li, Dong
2009
The Navier-Stokes equations in the critical Lebesgue space. Zbl 1216.35085
Dong, Hongjie; Du, Dapeng
2009
Regularity criteria for the dissipative quasi-geostrophic equations in Hölder spaces. Zbl 1185.35187
Dong, Hongjie; Pavlović, Nataša
2009
Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space. Zbl 1141.35436
Dong, Hongjie; Du, Dapeng
2008
Well-posedness for a transport equation with nonlocal velocity. Zbl 1170.35004
Dong, Hongjie
2008
Spatial analyticity of the solutions to the subcritical dissipative quasi-geostrophic equations. Zbl 1157.35456
Dong, Hongjie; Li, Dong
2008
On the Green’s matrices of strongly parabolic systems of second order. Zbl 1170.35005
Cho, Sungwon; Dong, Hongjie; Kim, Seick
2008
Finite time singularities for a class of generalized surface quasi-geostrophic equations. Zbl 1143.35084
Dong, Hongjie; Li, Dong
2008
On uniqueness of boundary blow-up solutions of a class of nonlinear elliptic equations. Zbl 1153.35039
Dong, Hongjie; Kim, Seick; Safonov, Mikhail
2008
The rate of convergence of finite-difference approximations for parabolic bellman equations with Lipschitz coefficients in cylindrical domains. Zbl 1127.65068
Dong, Hongjie; Krylov, Nicolai V.
2007
Partial regularity of solutions to the four-dimensional Navier-Stokes equations at the first blow-up time. Zbl 1156.35442
Dong, Hongjie; Du, Dapeng
2007
On the local smoothness of solutions of the Navier-Stokes equations. Zbl 1128.35081
Dong, Hongjie; Du, Dapeng
2007
Unique continuation for the Schrödinger equation with gradient vector potentials. Zbl 1119.35083
Dong, Hongjie; Staubach, Wolfgang
2007
On time-inhomogeneous controlled diffusion processes in domains. Zbl 1127.93062
Dong, Hongjie; Krylov, N. V.
2007
On the rate of convergence of finite-difference approximations for Bellman equations with constant coefficients. Zbl 1136.49312
Dong, Hongjie; Krylov, N. V.
2006
Hessian equations with elementary symmetric functions. Zbl 1237.35051
Dong, Hongjie
2006
Rate of convergence of finite-difference approximations for degenerate linear parabolic equations with $$C^1$$ and $$C^2$$ coefficients. Zbl 1085.65087
Dong, Hongjie; Krylov, Nicolai V.
2005
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Cited by 698 Authors

 76 Dong, Hongjie 24 Zheng, Shenzhou 23 Krylov, Nicolaĭ Vladimirovich 21 Kim, Doyoon 20 Kim, Seick 14 Choi, Jongkeun 13 Byun, Sun-Sig 12 Li, Dong 11 Kim, KyeongHun 11 Phan, Tuoc Van 9 Arkhipova, Arina A. Arkhipova 9 Wang, Lihe 9 Zhang, Junjie 8 Kim, Ildoo 8 Kim, Youchan 8 Mikulevicius, Remigijus 8 Tian, Hong 7 Bae, Hantaek 7 Gyöngy, István 7 Liu, Qiao 7 Mengesha, Tadele 7 Ryu, Seungjin 7 Xu, Longjuan 7 Yao, Fengping 7 Zhang, Hong 6 Biswas, Animikh 6 Carrillo de la Plata, José Antonio 6 Escauriaza Zubiria, Luis 6 Ferreira, Lucas Catão de Freitas 6 Geng, Jun 6 Li, Haigang 6 Martinez, Vincent R. 6 Stará, Jana 6 Wu, Jiahong 5 Constantin, Peter 5 Dai, Mimi 5 Dong, Boqing 5 Jolly, Michael S. 5 Kenig, Carlos Eduardo 5 Li, Zongyuan 5 Liang, Shuang 5 Niu, Weisheng 5 Ok, Jihoon 5 Softova, Lubomira G. 5 The Anh Bui 5 Xu, Yao 5 Yang, Dachun 5 Zhao, Jihong 5 Zhao, Zhiwen 4 Bertozzi, Andrea Louise 4 Chen, Zhimin 4 Dong, Rong 4 Granero Belinchón, Rafael 4 Guliyev, Vagif Sabir 4 Jang, Yunsoo 4 Jia, Yan 4 Kim, Hyunseok 4 Kriventsov, Dennis 4 Lazar, Omar 4 Lee, Mikyoung 4 Li, Dongsheng 4 Miao, Changxing 4 Mou, Chenchen 4 Nguyen Huy Tuan 4 Rodrigo, José Luis 4 Titi, Edriss Saleh 4 Vicol, Vlad C. 4 Wang, Weike 4 Wang, Yanqing 4 Wu, Gang 4 Yang, Sibei 4 Zhang, Zhijun 3 Albritton, Dallas 3 Bao, Jiguang 3 Barker, Tobias 3 Brown, Russell Murray 3 Bui, The Quan 3 Cho, Sungwon 3 Du, Dapeng 3 Duong, Xuan Thinh 3 Friedlander, Susan Jean 3 Han, Pigong 3 Hao, Xia 3 He, Jiawei 3 Hoffmann, Franca 3 Jakobsen, Espen Robstad 3 Jin, Tianling 3 Kang, Kyungkeun 3 Katzourakis, Nikolaos I. 3 Koch, Gabriel S. 3 Kohr, Mirela 3 Laurent, Thomas 3 Li, Kuijie 3 Mayboroda, Svitlana 3 Omarova, Mehriban N. 3 O’Regan, Donal 3 Palagachev, Dian K. 3 Park, Daehan 3 Pavlović, Nataša 3 Phonsom, C. ...and 598 more Authors
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Cited in 146 Serials

 60 Journal of Differential Equations 39 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 32 Journal of Mathematical Analysis and Applications 28 Journal of Functional Analysis 24 Calculus of Variations and Partial Differential Equations 20 Advances in Mathematics 20 SIAM Journal on Mathematical Analysis 20 Communications on Pure and Applied Analysis 19 Journal of Mathematical Fluid Mechanics 16 Transactions of the American Mathematical Society 16 Communications in Partial Differential Equations 15 Archive for Rational Mechanics and Analysis 15 Discrete and Continuous Dynamical Systems 14 Communications in Mathematical Physics 13 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 13 Potential Analysis 11 Mathematics of Computation 11 Applied Mathematics and Optimization 10 Journal de Mathématiques Pures et Appliquées. Neuvième Série 9 Proceedings of the American Mathematical Society 8 Nonlinearity 8 Journal of Evolution Equations 7 Analysis & PDE 6 Mathematical Methods in the Applied Sciences 6 Manuscripta Mathematica 6 Chinese Annals of Mathematics. Series B 6 Journal of Nonlinear Science 6 Acta Mathematica Sinica. English Series 6 Science China. Mathematics 5 Computers & Mathematics with Applications 5 Applied Mathematics Letters 5 NoDEA. Nonlinear Differential Equations and Applications 5 Nonlinear Analysis. Real World Applications 5 Boundary Value Problems 5 Stochastic and Partial Differential Equations. Analysis and Computations 4 SIAM Journal on Control and Optimization 4 Acta Mathematicae Applicatae Sinica. English Series 4 Journal of Mathematical Sciences (New York) 4 Communications in Contemporary Mathematics 4 Complex Variables and Elliptic Equations 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 The Annals of Probability 3 Mathematische Annalen 3 Mathematische Zeitschrift 3 Pacific Journal of Mathematics 3 Asymptotic Analysis 3 The Journal of Geometric Analysis 3 St. Petersburg Mathematical Journal 3 Discrete and Continuous Dynamical Systems. Series B 3 Advanced Nonlinear Studies 3 Evolution Equations and Control Theory 3 Annals of PDE 3 Journal of Elliptic and Parabolic Equations 2 Inverse Problems 2 Journal d’Analyse Mathématique 2 Journal of Mathematical Physics 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Duke Mathematical Journal 2 Journal of the Korean Mathematical Society 2 Mathematische Nachrichten 2 Monatshefte für Mathematik 2 Acta Applicandae Mathematicae 2 Physica D 2 Revista Matemática Iberoamericana 2 International Journal of Mathematics 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Stochastic Processes and their Applications 2 Journal of Dynamics and Differential Equations 2 Annales Academiae Scientiarum Fennicae. Mathematica 2 Abstract and Applied Analysis 2 Journal of Inequalities and Applications 2 Discrete Dynamics in Nature and Society 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Milan Journal of Mathematics 2 Multiscale Modeling & Simulation 2 Discrete and Continuous Dynamical Systems. Series S 2 Analysis and Mathematical Physics 2 Advances in Nonlinear Analysis 1 Communications on Pure and Applied Mathematics 1 Geophysical and Astrophysical Fluid Dynamics 1 Journal of Statistical Physics 1 Rocky Mountain Journal of Mathematics 1 Russian Mathematical Surveys 1 Ukrainian Mathematical Journal 1 Chaos, Solitons and Fractals 1 Theory of Probability and its Applications 1 Acta Mathematica 1 Annales Polonici Mathematici 1 Applied Mathematics and Computation 1 Canadian Journal of Mathematics 1 Indiana University Mathematics Journal 1 International Journal of Mathematics and Mathematical Sciences 1 Integral Equations and Operator Theory 1 Inventiones Mathematicae 1 Journal of the London Mathematical Society. Second Series 1 Journal of the Mathematical Society of Japan 1 Memoirs of the American Mathematical Society 1 Numerische Mathematik 1 Proceedings of the London Mathematical Society. Third Series 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II ...and 46 more Serials
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Cited in 37 Fields

 628 Partial differential equations (35-XX) 144 Fluid mechanics (76-XX) 52 Probability theory and stochastic processes (60-XX) 47 Harmonic analysis on Euclidean spaces (42-XX) 45 Functional analysis (46-XX) 38 Geophysics (86-XX) 36 Operator theory (47-XX) 29 Calculus of variations and optimal control; optimization (49-XX) 29 Numerical analysis (65-XX) 26 Real functions (26-XX) 24 Systems theory; control (93-XX) 22 Integral equations (45-XX) 22 Mechanics of deformable solids (74-XX) 12 Ordinary differential equations (34-XX) 11 Potential theory (31-XX) 11 Biology and other natural sciences (92-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Optics, electromagnetic theory (78-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Integral transforms, operational calculus (44-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Difference and functional equations (39-XX) 4 Operations research, mathematical programming (90-XX) 3 Measure and integration (28-XX) 3 Special functions (33-XX) 2 Functions of a complex variable (30-XX) 2 Differential geometry (53-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Topological groups, Lie groups (22-XX) 1 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 Statistics (62-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) 1 Astronomy and astrophysics (85-XX)