Regularity theory for the Isaacs equation through approximation methods

作     者：Pimentel, Edgard A. 

作者机构：Pontifical Catholic Univ Rio de Janeiro PUC Rio Dept Math BR-22451900 Rio De Janeiro RJ Brazil 

出 版 物：《ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE》 (Anna Inst Henri Poincare Anal. Non Lineaire)

年 卷 期：2019年第36卷第1期

页      面：53-74页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：PUC-Rio Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, FAPERJ, (E-26.200.002-2018/BBP) Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, FAPERJ 

主　　题：Isaacs equations Regularity theory Estimates in Sobolev and Holder spaces Approximation methods 

摘      要：In this paper, we propose an approximation method to study the regularity of solutions to the Isaacs equation. This class of problems plays a paramount role in the regularity theory for fully nonlinear elliptic equations. First, it is a model-problem of a non-convex operator. In addition, the usual mechanisms to access regularity of solutions fall short in addressing these equations. We approximate an Isaacs equation by a Bellman one, and make assumptions on the latter to recover information for the former. Our techniques produce results in Sobolev and Holder spaces;we also examine a few consequences of our main findings. (C) 2018 Elsevier Masson SAS. All rights reserved.