Sharp regularity for a singular fully nonlinear parabolic free boundary problem

被引：1

作者：

Araujo, Damiao J. ^{[1
]}

Sa, Ginaldo S. ^{[1
]}

Urbano, Jose Miguel ^{[2
,3
]}

机构：

[1] Univ Fed Paraiba, Dept Math, BR-58059900 Joao Pessoa, PB, Brazil

[2] King Abdullah Univ Sci & Technol KAUST, Appl Math & Computat Sci Program AMCS, Comp Elect & Math Sci & Engn Div CEMSE, Thuwal 239556900, Saudi Arabia

[3] Univ Coimbra, Dept Math, CMUC, P-3000143 Coimbra, Portugal

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 389卷

关键词：

Sharp regularity; Singular parabolic PDEs; Viscosity solutions; Free boundary; VISCOSITY SOLUTIONS;

D O I：

10.1016/j.jde.2024.01.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper establishes sharp local regularity estimates for viscosity solutions of fully nonlinear parabolic free boundary problems with singular absorption terms. The main difficulties are due to the blow-up of the source along the free boundary and the lack of a variational structure. The proof combines the power of the Ishii-Lions method with intrinsically parabolic oscillation estimates. The results are new, even for second-order linear operators in nondivergence form. (c) 2024 Elsevier Inc. All rights reserved.

引用

页码：90 / 113

页数：24

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