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## Karakhanyan, Aram L.

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 Author ID: karakhanyan.aram-l Published as: Karakhanyan, A.; Karakhanyan, A. L.; Karakhanyan, Aram; Karakhanyan, Aram L. Homepage: http://www.maths.ed.ac.uk/~aram/ External Links: MGP · Wikidata
 Documents Indexed: 32 Publications since 2004
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#### Co-Authors

 13 single-authored 6 Dipierro, Serena 4 Shahgholian, Henrik 4 Valdinoci, Enrico 2 Caffarelli, Luis Ángel 2 Strömqvist, Martin H. 1 Bucur, Claudia 1 Chaudhuri, Nirmalendu 1 Hakobyan, Artak S. 1 Kenig, Carlos Eduardo 1 Lin, Fang Hua 1 Sabra, Ahmad 1 Wang, Xu-Jia
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#### Serials

 3 Journal of Differential Equations 3 Communications in Partial Differential Equations 3 Calculus of Variations and Partial Differential Equations 2 Analysis & PDE 1 Archive for Rational Mechanics and Analysis 1 Advances in Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Applied Mathematics and Optimization 1 Journal of Differential Geometry 1 Journal of Functional Analysis 1 Manuscripta Mathematica 1 Monatshefte für Mathematik 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the American Mathematical Society 1 Transactions of the American Mathematical Society 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Journal of Elasticity 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Mathematical Analysis 1 Discrete and Continuous Dynamical Systems 1 Interfaces and Free Boundaries 1 Advanced Nonlinear Studies 1 Journal of Fixed Point Theory and Applications 1 Armenian Journal of Mathematics
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#### Fields

 31 Partial differential equations (35-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 4 Potential theory (31-XX) 3 Mechanics of deformable solids (74-XX) 3 Optics, electromagnetic theory (78-XX) 2 Fluid mechanics (76-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Number theory (11-XX) 1 Real functions (26-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Probability theory and stochastic processes (60-XX) 1 Operations research, mathematical programming (90-XX)

#### Citations contained in zbMATH

19 Publications have been cited 101 times in 77 Documents Cited by Year
The geometry of solutions to a segregation problem for nondivergence systems. Zbl 1217.35015
Caffarelli, L. A.; Karakhanyan, A. L.; Lin, Fang-Hua
2009
On the reflector shape design. Zbl 1201.53007
Karakhanyan, Aram; Wang, Xu-Jia
2010
Existence and regularity of the reflector surfaces in $$\mathbb R^{n+1}$$. Zbl 1298.35216
Karakhanyan, Aram L.
2014
The behavior of the free boundary near the fixed boundary for a minimization problem. Zbl 1111.35135
Karakhanyan, A. L.; Kenig, C. E.; Shahgholian, H.
2007
Stratification of free boundary points for a two-phase variational problem. Zbl 1394.35585
Dipierro, Serena; Karakhanyan, Aram L.
2018
An inverse problem for the refractive surfaces with parallel lighting. Zbl 1335.35086
Karakhanyan, Aram L.
2016
On the Lipschitz regularity of solutions of a minimum problem with free boundary. Zbl 1147.35116
Karakhanyan, Aram L.
2008
A class of unstable free boundary problems. Zbl 1368.35279
Dipierro, Serena; Karakhanyan, Aram; Valdinoci, Enrico
2017
Up-to boundary regularity for a singular perturbation problem of $$p$$-Laplacian type. Zbl 1159.35350
Karakhanyan, Aram L.
2006
A nonlinear free boundary problem with a self-driven Bernoulli condition. Zbl 1386.35488
Dipierro, Serena; Karakhanyan, Aram; Valdinoci, Enrico
2017
Optimal regularity for phase transition problems with convection. Zbl 1329.35361
Karakhanyan, Aram L.
2015
Application of uniform distribution to homogenization of a thin obstacle problem with $$p$$-Laplacian. Zbl 1304.35781
Karakhanyan, Aram L.; Strömqvist, Martin H.
2014
Sufficient conditions for regularity of area-preserving deformations. Zbl 1241.35197
Karakhanyan, Aram L.
2012
On derivation of Euler-Lagrange equations for incompressible energy-minimizers. Zbl 1183.35264
Chaudhuri, Nirmalendu; Karakhanyan, Aram L.
2009
A new discrete monotonicity formula with application to a two-phase free boundary problem in dimension two. Zbl 07024452
Dipierro, Serena; Karakhanyan, Aram L.
2018
On a conjecture of De Giorgi related to homogenization. Zbl 1382.34051
Karakhanyan, Aram L.; Shahgholian, Henrik
2017
New trends in free boundary problems. Zbl 1364.35444
Dipierro, Serena; Karakhanyan, Aram; Valdinoci, Enrico
2017
Lipschitz continuity of free boundary in the continuous casting problem with divergence form elliptic equation. Zbl 1317.35298
Karakhanyan, Aram L.
2016
On the regularity of weak solutions to refractor problem. Zbl 1281.35038
Karakhanyan, Aram
2009
Stratification of free boundary points for a two-phase variational problem. Zbl 1394.35585
Dipierro, Serena; Karakhanyan, Aram L.
2018
A new discrete monotonicity formula with application to a two-phase free boundary problem in dimension two. Zbl 07024452
Dipierro, Serena; Karakhanyan, Aram L.
2018
A class of unstable free boundary problems. Zbl 1368.35279
Dipierro, Serena; Karakhanyan, Aram; Valdinoci, Enrico
2017
A nonlinear free boundary problem with a self-driven Bernoulli condition. Zbl 1386.35488
Dipierro, Serena; Karakhanyan, Aram; Valdinoci, Enrico
2017
On a conjecture of De Giorgi related to homogenization. Zbl 1382.34051
Karakhanyan, Aram L.; Shahgholian, Henrik
2017
New trends in free boundary problems. Zbl 1364.35444
Dipierro, Serena; Karakhanyan, Aram; Valdinoci, Enrico
2017
An inverse problem for the refractive surfaces with parallel lighting. Zbl 1335.35086
Karakhanyan, Aram L.
2016
Lipschitz continuity of free boundary in the continuous casting problem with divergence form elliptic equation. Zbl 1317.35298
Karakhanyan, Aram L.
2016
Optimal regularity for phase transition problems with convection. Zbl 1329.35361
Karakhanyan, Aram L.
2015
Existence and regularity of the reflector surfaces in $$\mathbb R^{n+1}$$. Zbl 1298.35216
Karakhanyan, Aram L.
2014
Application of uniform distribution to homogenization of a thin obstacle problem with $$p$$-Laplacian. Zbl 1304.35781
Karakhanyan, Aram L.; Strömqvist, Martin H.
2014
Sufficient conditions for regularity of area-preserving deformations. Zbl 1241.35197
Karakhanyan, Aram L.
2012
On the reflector shape design. Zbl 1201.53007
Karakhanyan, Aram; Wang, Xu-Jia
2010
The geometry of solutions to a segregation problem for nondivergence systems. Zbl 1217.35015
Caffarelli, L. A.; Karakhanyan, A. L.; Lin, Fang-Hua
2009
On derivation of Euler-Lagrange equations for incompressible energy-minimizers. Zbl 1183.35264
Chaudhuri, Nirmalendu; Karakhanyan, Aram L.
2009
On the regularity of weak solutions to refractor problem. Zbl 1281.35038
Karakhanyan, Aram
2009
On the Lipschitz regularity of solutions of a minimum problem with free boundary. Zbl 1147.35116
Karakhanyan, Aram L.
2008
The behavior of the free boundary near the fixed boundary for a minimization problem. Zbl 1111.35135
Karakhanyan, A. L.; Kenig, C. E.; Shahgholian, H.
2007
Up-to boundary regularity for a singular perturbation problem of $$p$$-Laplacian type. Zbl 1159.35350
Karakhanyan, Aram L.
2006
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#### Cited by 78 Authors

 18 Karakhanyan, Aram L. 8 Dipierro, Serena 8 Wang, Kelei 6 Gutiérrez, Cristian E. 6 Valdinoci, Enrico 5 Jiang, Feida 5 Terracini, Susanna 5 Trudinger, Neil Sidney 5 Zilio, Alessandro 4 Liu, Jiakun 4 Zhang, Zhitao 3 Braga, J. Ederson M. 3 Dancer, Edward Norman 3 Liu, Zuhan 3 Sabra, Ahmad 3 Verzini, Gianmaria 3 Wei, Juncheng 3 Zhang, Shan 2 Andersson, John Erik 2 Berestycki, Henri 2 Caffarelli, Luis Ángel 2 De Silva, Daniela 2 Huang, Qingbo 2 Mikayelyan, Hayk 2 Quitalo, Veronica 2 Ricarte, Gleydson C. 2 Savin, Ovidiu V. 2 Shahgholian, Henrik 2 Xiang, Ni 1 Abedin, Farhan 1 Allen, Mark G. 1 Arakelyan, Avetik 1 Araújo, Janielly G. 1 Bazarganzadeh, Mahmoudreza 1 Bevan, Jonathan J. 1 Bozorgnia, Farid 1 Brix, Kolja 1 Gemmer, John A. 1 Gómez, Delfina 1 Guillen, Nestor 1 Guo, Xi 1 Hafizogullari, Yasemin 1 Huang, Yong 1 Kitagawa, Jun 1 Kriventsov, Dennis 1 Leitão, Raimundo A. 1 Li, YanYan 1 Lindgren, Erik 1 Liu, Yong 1 Lobo, Miguel Sousa 1 Matevosyan, Norayr 1 Mawi, Henok 1 Moon, Geeju 1 Moreira, Diego R. 1 Nguyen, Luc 1 Oliveira, J. Erivamberto L. 1 Patrizi, Stefania 1 Peirone, Roberto 1 Pérez, Eugenia 1 Platen, Andreas 1 Podolskii, Alexander V. 1 Ramos, Miguel P. N. 1 Raynor, S. G. 1 Rossi, Julio Daniel 1 Royo-Letelier, Jimena 1 Shaposhnikova, Tatiana A. 1 Silva, J. V. V. 1 Snelson, Stanley 1 Soave, Nicola 1 Strömqvist, Martin H. 1 Tavares, Hugo 1 Teymurazyan, Rafayel 1 Tournier, Federico 1 Tralli, Giulio 1 Wang, Peiyong 1 Xu, Jinju 1 Yang, Xiaoping 1 Zhou, Ling
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#### Cited in 35 Serials

 8 Calculus of Variations and Partial Differential Equations 7 Archive for Rational Mechanics and Analysis 5 Journal of Differential Equations 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 Discrete and Continuous Dynamical Systems 3 Advances in Mathematics 2 Arkiv för Matematik 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Journal of Functional Analysis 2 Mathematische Annalen 2 Transactions of the American Mathematical Society 2 Communications in Partial Differential Equations 2 Interfaces and Free Boundaries 2 Journal of the European Mathematical Society (JEMS) 2 Communications in Contemporary Mathematics 2 Analysis & PDE 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 Communications in Mathematical Physics 1 Communications on Pure and Applied Mathematics 1 Applied Mathematics and Optimization 1 Manuscripta Mathematica 1 Acta Applicandae Mathematicae 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Journal of Elasticity 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Mathematical Analysis 1 NoDEA. Nonlinear Differential Equations and Applications 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Acta Mathematica Sinica. English Series 1 Advanced Nonlinear Studies 1 Journal of Fixed Point Theory and Applications 1 Discrete and Continuous Dynamical Systems. Series S 1 Bulletin of Mathematical Sciences
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#### Cited in 24 Fields

 70 Partial differential equations (35-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 12 Optics, electromagnetic theory (78-XX) 8 Biology and other natural sciences (92-XX) 5 Operations research, mathematical programming (90-XX) 3 Quantum theory (81-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Potential theory (31-XX) 2 Ordinary differential equations (34-XX) 2 Differential geometry (53-XX) 2 Numerical analysis (65-XX) 2 Mechanics of deformable solids (74-XX) 1 Number theory (11-XX) 1 Real functions (26-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Systems theory; control (93-XX)