## Verchota, Gregory C.

Compute Distance To:
 Author ID: verchota.gregory-c Published as: Verchota, Gregory C.; Verchota, G. C.; Verchota, Gregory; Verchota, G.
 Documents Indexed: 34 Publications since 1984 Co-Authors: 11 Co-Authors with 19 Joint Publications 288 Co-Co-Authors
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### Co-Authors

 15 single-authored 7 Vogel, Andrew L. 6 Pipher, Jill Catherine 4 Kenig, Carlos Eduardo 3 Dahlberg, Bjorn E. J. 2 Fabes, Eugene B. 2 Griffin, Philip S. 1 Escauriaza Zubiria, Luis 1 Iwaniec, Tadeusz 1 Lewis, John L. 1 McConnell, Terry R. 1 Venouziou, Moises
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### Serials

 3 Proceedings of the American Mathematical Society 2 Annales de l’Institut Fourier 2 Duke Mathematical Journal 2 Indiana University Mathematics Journal 2 Journal of Functional Analysis 2 Transactions of the American Mathematical Society 1 Archive for Rational Mechanics and Analysis 1 Acta Mathematica 1 American Journal of Mathematics 1 Commentarii Mathematici Helvetici 1 Journal of Pure and Applied Algebra 1 Mathematische Annalen 1 Pacific Journal of Mathematics 1 Probability Theory and Related Fields 1 Revista Matemática Iberoamericana 1 The Journal of Geometric Analysis 1 Communications in Partial Differential Equations 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Potential Analysis 1 Mathematical Research Letters 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS)
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### Fields

 30 Partial differential equations (35-XX) 19 Potential theory (31-XX) 3 Operator theory (47-XX) 2 Number theory (11-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Probability theory and stochastic processes (60-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Functional analysis (46-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX)

### Citations contained in zbMATH Open

32 Publications have been cited 1,010 times in 600 Documents Cited by Year
Layer potentials and regularity for the Dirichlet problem for Laplace’s equation in Lipschitz domains. Zbl 0589.31005
Verchota, Gregory
1984
The Dirichlet problem for the Stokes system on Lipschitz domains. Zbl 0685.35085
Fabes, E. B.; Kenig, C. E.; Verchota, G. C.
1988
Boundary value problems for the systems of elastostatics in Lipschitz domains. Zbl 0699.35073
Dahlberg, B. E. J.; Kenig, C. E.; Verchota, G. C.
1988
On a regularity theorem for weak solutions to transmission problems with internal Lipschitz boundaries. Zbl 0761.35013
Escauriaza, L.; Fabes, E. B.; Verchota, G.
1992
The Dirichlet problem for the biharmonic equation in a Lipschitz domain. Zbl 0589.35040
Dahlberg, B. E. J.; Kenig, C. E.; Verchota, G. C.
1986
Area integral estimates for higher order elliptic equations and systems. Zbl 0892.35053
Dahlberg, Björn E. J.; Kenig, C. E.; Pipher, J.; Verchota, G. C.
1997
Dilation invariant estimates and the boundary Gårding inequality for higher order elliptic operators. Zbl 0878.35035
Pipher, Jill; Verchota, Gregory C.
1995
The biharmonic Neumann problem in Lipschitz domains. Zbl 1216.35021
Verchota, Gregory C.
2005
The Dirichlet problem in $$L^ p$$ for the biharmonic equation on Lipschitz domains. Zbl 0768.31006
Pipher, Jill; Verchota, Gregory
1992
The Dirichlet problem for the polyharmonic equation in Lipschitz domains. Zbl 0724.31005
Verchota, Gregory
1990
A maximum principle for biharmonic functions in Lipschitz and $$C^ 1$$ domains. Zbl 0794.31005
Pipher, J.; Verchota, G.
1993
The Dirichlet problem for the biharmonic equation in $$C^ 1$$ domains. Zbl 0644.35039
Verchota, Gregory
1987
Maximum principles for the polyharmonic equation on Lipschitz domains. Zbl 0844.35013
Pipher, J.; Verchota, G. C.
1995
The failure of rank-one connections. Zbl 1007.35014
Iwaniec, Tadeusz; Verchota, Gregory C.; Vogel, Andrew L.
2002
Nonsymmetric systems on nonsmooth planar domains. Zbl 0892.35055
Verchota, G. C.; Vogel, A. L.
1997
Area integral estimates for the biharmonic operator in Lipschitz domains. Zbl 0774.35022
Pipher, Jill; Verchota, Gregory
1991
Potentials for the Dirichlet problem in Lipschitz domains. Zbl 0858.35033
Verchota, Gregory C.
1996
Wolff snowflakes. Zbl 1108.31006
Lewis, John L.; Verchota, Gregory C.; Vogel, Andrew L.
2005
Conditioned Brownian motion in simply connected planar domains. Zbl 0777.60073
Griffin, Philip S.; McConnell, Terry R.; Verchota, Gregory
1993
Harmonic homeomorphisms of the closed disc to itself need be in $$W^{1,p}$$, $$p<2$$, but not $$W^{1,2}$$. Zbl 1109.31007
Verchota, Gregory C.
2007
The multidirectional Neumann problem in $$\mathbb R^{4}$$. Zbl 1102.31008
Verchota, Gregory C.; Vogel, Andrew L.
2006
The mixed problem for harmonic functions in polyhedra of $$\mathbb R^3$$. Zbl 1160.35022
Venouziou, Moises; Verchota, Gregory C.
2008
Boundary coerciveness and the Neumann problem for 4th order linear partial differential operators. Zbl 1183.47042
Verchota, Gregory C.
2010
The use of Rellich identities on certain nongraph boundaries. Zbl 1007.31004
Verchota, Gregory
2001
A multidirectional Dirichlet problem. Zbl 1274.35096
Verchota, Gregory C.; Vogel, Andrew L.
2003
Remarks on 2nd order elliptic systems in Lipschitz domains. Zbl 0662.35034
Verchota, G. C.
1986
Distortion of area and conditioned Brownian motion. Zbl 0794.60081
Griffin, P. S.; Verchota, G. C.; Vogel, A. L.
1993
Nonsymmetric systems and area integral estimates. Zbl 0941.35022
Verchota, G. C.; Vogel, A. L.
2000
Noncoercive sums of squares in $$\mathbb R[x_1,\ldots ,x_n]$$. Zbl 1272.12005
Verchota, Gregory C.
2010
Nonvariational layer potentials with respect to Hölder continuous vector fields. Zbl 1220.35034
Verchota, Gregory C.
2007
Counterexamples and uniqueness for $$L^{p}(\partial \Omega )$$ oblique derivative problems. Zbl 1136.35023
Verchota, Gregory C.
2007
Agmon coerciveness and the analysis of operators with formally positive integro-differential forms. Zbl 1252.47041
Verchota, Gregory C.
2012
Agmon coerciveness and the analysis of operators with formally positive integro-differential forms. Zbl 1252.47041
Verchota, Gregory C.
2012
Boundary coerciveness and the Neumann problem for 4th order linear partial differential operators. Zbl 1183.47042
Verchota, Gregory C.
2010
Noncoercive sums of squares in $$\mathbb R[x_1,\ldots ,x_n]$$. Zbl 1272.12005
Verchota, Gregory C.
2010
The mixed problem for harmonic functions in polyhedra of $$\mathbb R^3$$. Zbl 1160.35022
Venouziou, Moises; Verchota, Gregory C.
2008
Harmonic homeomorphisms of the closed disc to itself need be in $$W^{1,p}$$, $$p<2$$, but not $$W^{1,2}$$. Zbl 1109.31007
Verchota, Gregory C.
2007
Nonvariational layer potentials with respect to Hölder continuous vector fields. Zbl 1220.35034
Verchota, Gregory C.
2007
Counterexamples and uniqueness for $$L^{p}(\partial \Omega )$$ oblique derivative problems. Zbl 1136.35023
Verchota, Gregory C.
2007
The multidirectional Neumann problem in $$\mathbb R^{4}$$. Zbl 1102.31008
Verchota, Gregory C.; Vogel, Andrew L.
2006
The biharmonic Neumann problem in Lipschitz domains. Zbl 1216.35021
Verchota, Gregory C.
2005
Wolff snowflakes. Zbl 1108.31006
Lewis, John L.; Verchota, Gregory C.; Vogel, Andrew L.
2005
A multidirectional Dirichlet problem. Zbl 1274.35096
Verchota, Gregory C.; Vogel, Andrew L.
2003
The failure of rank-one connections. Zbl 1007.35014
Iwaniec, Tadeusz; Verchota, Gregory C.; Vogel, Andrew L.
2002
The use of Rellich identities on certain nongraph boundaries. Zbl 1007.31004
Verchota, Gregory
2001
Nonsymmetric systems and area integral estimates. Zbl 0941.35022
Verchota, G. C.; Vogel, A. L.
2000
Area integral estimates for higher order elliptic equations and systems. Zbl 0892.35053
Dahlberg, Björn E. J.; Kenig, C. E.; Pipher, J.; Verchota, G. C.
1997
Nonsymmetric systems on nonsmooth planar domains. Zbl 0892.35055
Verchota, G. C.; Vogel, A. L.
1997
Potentials for the Dirichlet problem in Lipschitz domains. Zbl 0858.35033
Verchota, Gregory C.
1996
Dilation invariant estimates and the boundary Gårding inequality for higher order elliptic operators. Zbl 0878.35035
Pipher, Jill; Verchota, Gregory C.
1995
Maximum principles for the polyharmonic equation on Lipschitz domains. Zbl 0844.35013
Pipher, J.; Verchota, G. C.
1995
A maximum principle for biharmonic functions in Lipschitz and $$C^ 1$$ domains. Zbl 0794.31005
Pipher, J.; Verchota, G.
1993
Conditioned Brownian motion in simply connected planar domains. Zbl 0777.60073
Griffin, Philip S.; McConnell, Terry R.; Verchota, Gregory
1993
Distortion of area and conditioned Brownian motion. Zbl 0794.60081
Griffin, P. S.; Verchota, G. C.; Vogel, A. L.
1993
On a regularity theorem for weak solutions to transmission problems with internal Lipschitz boundaries. Zbl 0761.35013
Escauriaza, L.; Fabes, E. B.; Verchota, G.
1992
The Dirichlet problem in $$L^ p$$ for the biharmonic equation on Lipschitz domains. Zbl 0768.31006
Pipher, Jill; Verchota, Gregory
1992
Area integral estimates for the biharmonic operator in Lipschitz domains. Zbl 0774.35022
Pipher, Jill; Verchota, Gregory
1991
The Dirichlet problem for the polyharmonic equation in Lipschitz domains. Zbl 0724.31005
Verchota, Gregory
1990
The Dirichlet problem for the Stokes system on Lipschitz domains. Zbl 0685.35085
Fabes, E. B.; Kenig, C. E.; Verchota, G. C.
1988
Boundary value problems for the systems of elastostatics in Lipschitz domains. Zbl 0699.35073
Dahlberg, B. E. J.; Kenig, C. E.; Verchota, G. C.
1988
The Dirichlet problem for the biharmonic equation in $$C^ 1$$ domains. Zbl 0644.35039
Verchota, Gregory
1987
The Dirichlet problem for the biharmonic equation in a Lipschitz domain. Zbl 0589.35040
Dahlberg, B. E. J.; Kenig, C. E.; Verchota, G. C.
1986
Remarks on 2nd order elliptic systems in Lipschitz domains. Zbl 0662.35034
Verchota, G. C.
1986
Layer potentials and regularity for the Dirichlet problem for Laplace’s equation in Lipschitz domains. Zbl 0589.31005
Verchota, Gregory
1984
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### Cited by 563 Authors

 37 Mitrea, Marius 26 Kang, Hyeonbae 24 Wendland, Wolfgang L. 23 Medková, Dagmar 21 Kohr, Mirela 20 Shen, Zhongwei 18 Mitrea, Irina 17 Ammari, Habib M. 17 Kenig, Carlos Eduardo 17 Verchota, Gregory C. 14 Mitrea, Dorina 13 Brown, Russell Murray 13 Hofmann, Steve 13 Mayboroda, Svitlana 13 Pipher, Jill Catherine 12 Lim, Mikyoung 10 Maz’ya, Vladimir Gilelevich 9 Agranovich, Mikhail Semënovich 9 Barton, Ariel 9 Dindoš, Martin 8 Ando, Kazunori 8 Chang, Tongkeun 8 Lee, Hyundae 7 Krutitskii, Pavel A. 7 Vogel, Andrew L. 6 Chandler-Wilde, Simon N. 6 Geng, Jun 6 Lewis, John L. 6 Ott, Katharine A. 6 Pintea, Cornel 6 Qian, Tao 6 Russo, Antonio 6 Seo, Jin Keun 6 Tartaglione, Alfonsina 6 Taylor, Michael Eugene 5 Auscher, Pascal 5 Axelsson, Andreas 5 Du, Zhihua 5 Kim, Kyoungsun 5 Lanza de Cristoforis, Massimo 5 Méndez, Osvaldo 5 Mikhailov, Sergey E. 5 Varnhorn, Werner 5 Xie, Hehu 5 Yang, Sibei 5 Yu, SangHyeon 5 Zaitsev, A. B. 5 Zribi, Habib 4 Beretta, Elena 4 Choe, Hi Jun 4 Dahlberg, Bjorn E. J. 4 Dahlke, Stephan 4 Feng, Xiaobing 4 Jiang, Shidong 4 Jung, Younghoon 4 Kim, Doyoon 4 Martell, José María (Chema) 4 Miyanishi, Yoshihisa 4 Onninen, Jani 4 Perfekt, Karl-Mikael 4 Rokhlin, Vladimir 4 Russo, Remigio 4 Spence, Euan A. 4 Sweers, Guido H. 4 Toro, Tatiana 4 Zhuge, Jinping 3 Akman, Murat 3 Amrouche, Chérif 3 Aspri, Andrea 3 Badger, Matthew 3 Bagapsh, A. O. 3 Baratchart, Laurent 3 Carcione, José M. 3 Chasman, L. Mercredi 3 Choi, Doosung 3 Dacorogna, Bernard 3 Deuring, Paul 3 Dong, Hongjie 3 Escauriaza Zubiria, Luis 3 Fabes, Eugene B. 3 Graham, Ivan G. 3 Groşan, Teodor S. 3 Gutt, Robert 3 Helsing, Johan 3 Iwaniec, Tadeusz 3 Ji, Yong-Gwan 3 Kapanadze, David 3 Kilty, Joel 3 Kim, Seick 3 Lanzani, Loredana 3 Lin, Fang Hua 3 Lindner, Marko 3 Liu, Hongyu 3 Marcellini, Paolo 3 Melenk, Jens Markus 3 Natroshvili, David 3 Nistor, Victor 3 Paolini, Emanuele 3 Praetorius, Dirk 3 Qiao, Yu ...and 463 more Authors
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### Cited in 161 Serials

 29 Journal of Differential Equations 29 Transactions of the American Mathematical Society 28 Journal of Functional Analysis 25 Journal of Mathematical Analysis and Applications 19 Potential Analysis 16 Archive for Rational Mechanics and Analysis 16 Communications in Partial Differential Equations 15 Applicable Analysis 15 Mathematical Methods in the Applied Sciences 12 Proceedings of the American Mathematical Society 11 Integral Equations and Operator Theory 10 Mathematische Annalen 10 Journal of Integral Equations and Applications 10 Journal de Mathématiques Pures et Appliquées. Neuvième Série 10 Complex Variables and Elliptic Equations 8 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 8 SIAM Journal on Mathematical Analysis 7 Functional Analysis and its Applications 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Revista Matemática Iberoamericana 6 Computer Methods in Applied Mechanics and Engineering 6 Communications on Pure and Applied Mathematics 6 Advances in Mathematics 6 Duke Mathematical Journal 6 Inventiones Mathematicae 6 Numerische Mathematik 6 Journal of Mathematical Sciences (New York) 6 The Journal of Fourier Analysis and Applications 6 Journal of Mathematical Fluid Mechanics 5 Journal d’Analyse Mathématique 5 Mathematical Notes 5 Mathematics of Computation 5 Calculus of Variations and Partial Differential Equations 4 Communications in Mathematical Physics 4 Journal of Computational Physics 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Annales de l’Institut Fourier 4 Manuscripta Mathematica 4 Mathematische Nachrichten 4 Zeitschrift für Analysis und ihre Anwendungen 4 Numerical Methods for Partial Differential Equations 4 Journal of Elasticity 4 Russian Journal of Mathematical Physics 4 Applied and Computational Harmonic Analysis 3 Inverse Problems 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Czechoslovak Mathematical Journal 3 Journal of Computational and Applied Mathematics 3 Memoirs of the American Mathematical Society 3 Numerical Functional Analysis and Optimization 3 Acta Applicandae Mathematicae 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Journal of the American Mathematical Society 3 The Journal of Geometric Analysis 3 SIAM Journal on Applied Mathematics 3 Russian Mathematics 3 SIAM Journal on Scientific Computing 3 Advances in Computational Mathematics 3 Annales Academiae Scientiarum Fennicae. Mathematica 3 Acta Mathematica Sinica. English Series 3 Complex Analysis and Operator Theory 3 Analysis & PDE 3 Bulletin of Mathematical Sciences 2 Bulletin of the Australian Mathematical Society 2 Computers & Mathematics with Applications 2 Arkiv för Matematik 2 Applied Mathematics and Computation 2 Mathematische Zeitschrift 2 Ricerche di Matematica 2 Advances in Applied Mathematics 2 Applied Numerical Mathematics 2 Applied Mathematics Letters 2 Forum Mathematicum 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Computational Mathematics and Mathematical Physics 2 Journal of Dynamics and Differential Equations 2 Engineering Analysis with Boundary Elements 2 Discrete and Continuous Dynamical Systems 2 Taiwanese Journal of Mathematics 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Journal of the European Mathematical Society (JEMS) 2 Communications in Contemporary Mathematics 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Communications on Pure and Applied Analysis 2 Analysis and Applications (Singapore) 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Proceedings of the Steklov Institute of Mathematics 2 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 2 Inverse Problems and Imaging 2 Discrete and Continuous Dynamical Systems. Series S 1 Journal of Mathematical Physics 1 Lithuanian Mathematical Journal 1 Acta Mathematica 1 Aplikace Matematiky 1 Applied Mathematics and Optimization 1 BIT 1 Computing 1 Illinois Journal of Mathematics 1 International Journal of Mathematics and Mathematical Sciences 1 International Journal for Numerical Methods in Engineering ...and 61 more Serials
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### Cited in 43 Fields

 471 Partial differential equations (35-XX) 133 Potential theory (31-XX) 89 Fluid mechanics (76-XX) 85 Numerical analysis (65-XX) 61 Mechanics of deformable solids (74-XX) 56 Harmonic analysis on Euclidean spaces (42-XX) 52 Operator theory (47-XX) 46 Functional analysis (46-XX) 41 Integral equations (45-XX) 32 Functions of a complex variable (30-XX) 29 Optics, electromagnetic theory (78-XX) 25 Global analysis, analysis on manifolds (58-XX) 15 Probability theory and stochastic processes (60-XX) 12 Measure and integration (28-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 6 Real functions (26-XX) 5 Approximations and expansions (41-XX) 5 Geophysics (86-XX) 4 Special functions (33-XX) 4 Quantum theory (81-XX) 3 Manifolds and cell complexes (57-XX) 3 Information and communication theory, circuits (94-XX) 2 Combinatorics (05-XX) 2 Number theory (11-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Ordinary differential equations (34-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral transforms, operational calculus (44-XX) 2 Convex and discrete geometry (52-XX) 2 Differential geometry (53-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Biology and other natural sciences (92-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Topological groups, Lie groups (22-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 General topology (54-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Systems theory; control (93-XX)