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

被引：4

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, Argentina

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

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2023年 / 171卷

基金：

欧盟地平线“2020”;

关键词：

Free boundary regularity; Singular; degenerate operator; Non-zero right hand side; Viscosity solutions; Harnack inequality; Optimal regularity; FLAT FREE-BOUNDARIES; NONLINEAR ELLIPTIC-OPERATORS; 2-PHASE PROBLEMS; VISCOSITY SOLUTIONS; MINIMUM PROBLEM; C-1; C-ALPHA REGULARITY; VARIABLE EXPONENT; WEAK SOLUTIONS; EQUATIONS; 2ND-ORDER;

D O I：

10.1016/j.matpur.2022.12.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We continue our study in [24] on viscosity solutions to a one-phase free boundary problem for the p(x)-Laplacian with non-zero right hand side. We first prove that viscosity solutions are locally Lipschitz continuous, which is the optimal regularity for the problem. Then we prove that Lipschitz free boundaries of viscosity solutions are C1, alpha. We also present some applications of our results. Moreover, we obtain new results for the operator under consideration that are of independent interest, such as a Harnack inequality.(c) 2022 Elsevier Masson SAS. All rights reserved.

引用

页码：26 / 74

页数：49

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