The inhomogeneous boundary Harnack principle for fully nonlinear and p-Laplace equations

被引：3

作者：

Allen, Mark ^{[1
]}

Kriventsov, Dennis ^{[2
]}

Shahgholian, Henrik ^{[3
]}

机构：

[1] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

[2] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

[3] KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2023年 / 40卷 / 01期

关键词：

Nonlinear equations; p-Laplace equations; HARMONIC-FUNCTIONS; MARTIN BOUNDARY; LIPSCHITZ; BEHAVIOR;

D O I：

10.4171/AIHPC/40

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a boundary Harnack principle in Lipschitz domains with small constant for fully nonlinear and p-Laplace-type equations with a right-hand side, as well as for the Laplace equa-tion on nontangentially accessible domains under extra conditions. The approach is completely new and gives a systematic approach for proving similar results for a variety of equations and geometries.

引用

页码：133 / 156

页数：24

共 13 条

[1] Boundary Harnack principle and Martin boundary for a uniform domain
Aikawa, H
[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2001, 53 (01) : 119 - 145
[2] Aikawa H., 2006, Harmonic analysis and its applications, P1
[3] A New Boundary Harnack Principle (Equations with Right Hand Side)
Allen, Mark
Shahgholian, Henrik
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2019, 234 (03) : 1413 - 1444
[4] Caffarelli S., 2005, A geometric approach to free boundary prob- lems, volume 68 of Graduate Studies in Mathematics, V68, P13, DOI DOI 10.1090/GSM/068
[5] USERS GUIDE TO VISCOSITY SOLUTIONS OF 2ND-ORDER PARTIAL-DIFFERENTIAL EQUATIONS
CRANDALL, MG
ISHII, H
LIONS, PL
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 27 (01) : 1 - 67
[6] Feldman M, 2001, INDIANA U MATH J, V50, P1171
[7] Gilbarg D., 2001, ELLIPTIC PARTIAL DIF
[8] Giusti Enrico, 2003, DIRECT METHODS CALCU, DOI 10.1142/9789812795557
[9] BOUNDARY-BEHAVIOR OF HARMONIC-FUNCTIONS IN NON-TANGENTIALLY ACCESSIBLE DOMAINS
JERISON, DS
KENIG, CE
[J]. ADVANCES IN MATHEMATICS, 1982, 46 (01) : 80 - 147
[10] Boundary behavior and the Martin boundary problem for p harmonic functions in Lipschitz domains
Lewis, John
Nystrom, Kaj
[J]. ANNALS OF MATHEMATICS, 2010, 172 (03) : 1907 - 1948

← 1 2 →