Free boundary theory for singular/degenerate nonlinear equations with right hand side: a non-variational approach

被引：7

作者：

Braga, J. Ederson M. ^{[1
]}

Leitao, Raimundo A. ^{[1
]}

Oliveira, J. Erivamberto L. ^{[1
]}

机构：

[1] Univ Fed Ceara, Dept Matemat, Campus Pici Bloco 914, BR-60455760 Fortaleza, Ceara, Brazil

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2020年 / 59卷 / 02期

关键词：

2-PHASE PROBLEMS; MINIMUM PROBLEM; VISCOSITY SOLUTIONS; ELLIPTIC-EQUATIONS; WEAK SOLUTIONS; REGULARITY; EQUIVALENCE;

D O I：

10.1007/s00526-020-01733-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use non-variational type arguments to prove optimal regularity and smoothness of the free boundary for one-phase solutions to inhomogeneous nonlinear free boundary problems (FBP) governed by singular/degenerate elliptic PDEs with a nonzero right hand side (RHS). In a precise way, we show that viscosity solutions to FBP, as previously mentioned, are locally Lipschitz continuous and under certain conditions, flat or Lipschitz free boundaries, are C-1,C-alpha.

引用

页数：29

共 11 条

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Leitao, Raimundo
Ricarte, Gleydson
INTERFACES AND FREE BOUNDARIES, 2018, 20 (04) : 577 - 595
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