Regularity of flat free boundaries for a p(x)-Laplacian problem with right hand side

被引：10

作者：

Ferrari, Fausto ^{[1
]}

Lederman, Claudia ^{[2
,3
]}

机构：

[1] Univ Bologna, Dipartimento Matemat, Piazza Porta S Donato 5, I-40126 Bologna, Italy

[2] Univ Buenos Aires, Fac Ciencias Exactas & Nat, IMAS, CONICET, RA-1428 Buenos Aires, DF, Argentina

[3] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, RA-1428 Buenos Aires, DF, Argentina

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2021年 / 212卷

基金：

欧盟地平线“2020”;

关键词：

Free boundary problem; Singular/degenerate operator; Variable exponent spaces; Regularity of the free boundary; Non-zero right hand side; Viscosity solutions; LIPSCHITZ FREE-BOUNDARIES; NONLINEAR ELLIPTIC-EQUATIONS; SINGULARLY PERTURBED EQUATIONS; 2-PHASE PROBLEMS; VISCOSITY SOLUTIONS; MINIMUM PROBLEM; VARIABLE EXPONENT; WEAK SOLUTIONS; 2ND-ORDER; FUNCTIONALS;

D O I：

10.1016/j.na.2021.112444

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider viscosity solutions to a one-phase free boundary problem for the p(x)-Laplacian with non-zero right hand side. We apply the tools developed in De Silva (2011) to prove that flat free boundaries are C-1,C-alpha. Moreover, we obtain some new results for the operator under consideration that are of independent interest. (C) 2021 Elsevier Ltd. All rights reserved.

引用

页数：25

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