Obstacle problem for a non-convex fully nonlinear operator

被引：6

作者：

Lee, Ki-Ahm ^{[1
,2
]}

Park, Jinwan ^{[1
]}

机构：

[1] Seoul Natl Univ, Seoul 08826, South Korea

[2] Korea Inst Adv Study, Seoul 02455, South Korea

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2018年 / 265卷 / 11期

基金：

新加坡国家研究基金会;

关键词：

Free boundary problem; Obstacle problem; Regularity of free boundary; Non-convex fully nonlinear operator; Evans-Krylov theorem; FREE-BOUNDARY PROBLEMS; MONGE-AMPERE EQUATION; ELLIPTIC-EQUATIONS; REGULARITY;

D O I：

10.1016/j.jde.2018.07.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study a priori C-2,C-alpha estimate up to the boundary for F(D(2)u) = 0 and the regularity of the free boundary of the obstacle problem for fully nonlinear operator under specific conditions for the operator and level sets of the operator. The conditions are variations of conditions for the zero set of the operator in [7]. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：5809 / 5830

页数：22

共 50 条

[1] The regularity theory for the double obstacle problem for fully nonlinear operator
Lee, Ki-Ahm
Park, Jinwan
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2023, 235
[2] THE OBSTACLE PROBLEM FOR MONGE-AMPERE TYPE EQUATIONS IN NON-CONVEX DOMAINS
Xiong, Jingang
Bao, Jiguang
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2011, 10 (01) : 59 - 68
[3] MINIMAX THEOREMS IN A FULLY NON-CONVEX SETTING
Ricceri, Biagio
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS, 2019, 3 (01): : 45 - 52
[4] Non-Convex Feature Learning via Operator
Kong, Deguang
Ding, Chris
PROCEEDINGS OF THE TWENTY-EIGHTH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE, 2014, : 1918 - 1924
[5] NON-CONVEX GENERALIZATION OF THE CIRCLE PROBLEM
NOWAK, WG
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1980, 314 : 136 - 145
[6] Solving a nonlinear non-convex trim loss problem with a genetic hybrid algorithm
Östermark, R
COMPUTERS & OPERATIONS RESEARCH, 1999, 26 (06) : 623 - 635
[7] The convex envelope is the solution of a nonlinear obstacle problem
Oberman, Adam M.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (06) : 1689 - 1694
[8] Nonlinear Non-convex Optimization of Hydraulic Networks
Tahavori, Maryamsadat
Kallesoe, Carsten
Leth, John
Wisniewski, Rafael
2013 IEEE INTERNATIONAL CONFERENCE ON CONTROL APPLICATIONS (CCA), 2013, : 894 - 898
[9] A NON-CONVEX ANALOGON AND THE MULTIDIMENSIONAL SPHERE PROBLEM
NOWAK, WG
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1983, 338 : 149 - 165
[10] VARIATIONAL PROBLEM IN DUALITY FOR NON-CONVEX CASES
EKELAND, I
LASRY, JM
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1980, 291 (08): : 493 - 496

← 1 2 3 4 5 →