OPTIMAL BOUNDARY REGULARITY AND A HOPF-TYPE LEMMA FOR DIRICHLET PROBLEMS INVOLVING THE LOGARITHMIC LAPLACIAN

被引：0

作者：

Hernandez-Santamaria, Victor ^{[1
]}

Rios, Luis Fernando Lopez ^{[2
]}

Saldana, Alberto ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Circuito Exterior,Ciudad Univ, Coyoacan 04510, Ciudad De Mexic, Mexico

[2] Univ Nacl Autonoma Mexico, Inst Invest Matemat Aplicadas & Sistemas, Circuito Escolar S-N,Ciudad Univ, Ciudad De Mexico 04510, Mexico

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2025年 / 45卷 / 01期

关键词：

Hopf lemma; Kelvin transform; uniqueness by convexity; GREEN-FUNCTION;

D O I：

10.3934/dcds.2024084

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the optimal boundary regularity of solutions to Dirichlet problems involving the logarithmic Laplacian. Our proofs are based on the construction of suitable barriers via the Kelvin transform and direct computations. As applications of our results, we show a Hopf-type lemma for nonnegative weak solutions and the uniqueness of solutions to some nonlinear problems.

引用

页码：1 / 36

页数：36

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