Uniform Lipschitz estimates up to the boundary for singular perturbation problem for some nonlinear elliptic PDEs with unbounded ingredients

被引：0

作者：

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

Carneiro, J. Gleison ^{[2
]}

Moreira, Diego R. ^{[1
]}

机构：

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

[2] Univ Fed Ceara, Dept Matemat, Cidade Univ, BR-62900000 Russas, CE, Brazil

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2023年 / 232卷

关键词：

Singular perturbation problem; Lipschitz regularity; Nonlinear operators; Boundary estimates; VISCOSITY SOLUTIONS; REGULARITY;

D O I：

10.1016/j.na.2023.113283

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove uniform up to the boundary gradient estimates for one phase nonlinear inhomogeneous singular perturbation problems with unbounded measurable ingre-dients governed by fully nonlinear elliptic equations. We present similar results for quasilinear PDEs with bounded RHS. Our proof is based on the Lipschitz regularity up to the boundary for free boundary problems (FBP) found in Braga and Moreira (2022).& COPY; 2023 Elsevier Ltd. All rights reserved.

引用

页数：19

共 18 条

[1] Berestycki H., 1988, ANAL PARTIAL DIFFERE, V122, P567
[2] Up to the boundary gradient estimates for viscosity solutions to nonlinear free boundary problems with unbounded measurable ingredients
Braga, J. Ederson M.
Moreira, Diego R.
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2022, 61 (05)
[3] Gradient estimates for variable coefficient parabolic equations and singular perturbation problems
Caffarelli, LA
Kenig, CE
[J]. AMERICAN JOURNAL OF MATHEMATICS, 1998, 120 (02) : 391 - 439
[4] Caffarelli LA, 1997, INDIANA U MATH J, V46, P719
[5] Caffarelli LA, 1997, INDIANA U MATH J, V46, P453
[6] Giusti E., 2003, Direct methods in the Calculus of Variations, DOI 10.1142/9789812795557
[7] Gurevich A, 1999, COMMUN PUR APPL MATH, V52, P363
[8] Up-to boundary regularity for a singular perturbation problem of p-Laplacian type
Karakhanyan, AL
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 226 (02) : 558 - 571
[9] Weak Harnack inequality for fully nonlinear uniformly elliptic PDE with unbounded ingredients
Koike, Shigeaki
Swiech, Andrzej
[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2009, 61 (03) : 723 - 755
[10] Lederman C., 1998, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), V27, P253

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