The obstacle problem for a fractional Monge-Ampere equation

被引：2

作者：

Jhaveri, Yash ^{[1
]}

Stinga, Pablo Raul ^{[2
]}

机构：

[1] Inst Adv Study, Sch Math, Princeton, NJ 08540 USA

[2] Iowa State Univ, Dept Math, 396 Carver Hall, Ames, IA 50011 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2020年 / 45卷 / 06期

关键词：

Free boundary problem; regularity; fractional Monge-Ampere equation; degenerate elliptic nonlinear nonlocal equation; ELLIPTIC-EQUATIONS; REGULARITY;

D O I：

10.1080/03605302.2019.1697885

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the obstacle problem for a nonlocal, degenerate elliptic Monge-Ampere equation. We show existence and regularity of a unique classical solution to the problem and regularity of the free boundary.

引用

页码：457 / 482

页数：26

共 15 条

[1] The Evans-Krylov theorem for nonlocal fully nonlinear equations
Caffarell, Luis
Silvestre, Luis
[J]. ANNALS OF MATHEMATICS, 2011, 174 (02) : 1163 - 1187
[2] Caffarelli L., 2015, Ann. PDE, V1, P1
[3] Obstacle problems for integro-differential operators: regularity of solutions and free boundaries
Caffarelli, Luis
Ros-Oton, Xavier
Serra, Joaquim
[J]. INVENTIONES MATHEMATICAE, 2017, 208 (03) : 1155 - 1211
[4] Regularity Results for Nonlocal Equations by Approximation
Caffarelli, Luis
Silvestre, Luis
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2011, 200 (01) : 59 - 88
[5] Regularity Theory for Fully Nonlinear Integro-Differential Equations
Caffarelli, Luis
Silvestre, Luis
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2009, 62 (05) : 597 - 638
[6] Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
Caffarelli, Luis A.
Salsa, Sandro
Silvestre, Luis
[J]. INVENTIONES MATHEMATICAE, 2008, 171 (02) : 425 - 461
[7] All functions are locally s-harmonic up to a small error
Dipierro, Serena
Savin, Ovidiu
Valdinoci, Enrico
[J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2017, 19 (04) : 957 - 966
[8] Aleksandrov-Bakelman-Pucci Type Estimates for Integro-Differential Equations
Guillen, Nestor
Schwab, Russell W.
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2012, 206 (01) : 111 - 157
[9] C1,α Interior Regularity for Nonlinear Nonlocal Elliptic Equations with Rough Kernels
Kriventsov, Dennis
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2013, 38 (12) : 2081 - 2106
[10] The obstacle problem for Monge-Ampere equation
Lee, K
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2001, 26 (1-2) : 33 - 42

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