ON THE FIRST EIGENVALUE OF THE NORMALIZED p-LAPLACIAN

被引：1

作者：

Crasta, Graziano ^{[1
]}

Fragala, Ilaria ^{[2
]}

Kawohl, Bernd ^{[3
]}

机构：

[1] Univ Roma I, Dipartimento Matemat G Castelnuovo, Piazzale Aldo Moro 2, I-00185 Rome, Italy

[2] Politecn Milan, Dipartimento Matemat, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy

[3] Univ Cologne, Math Inst, D-50923 Cologne, Germany

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2020年 / 148卷 / 02期

关键词：

Normalized p-Laplacian; viscosity solutions; eigenvalue problem; TUG-OF-WAR; MAXIMUM PRINCIPLE; VISCOSITY SOLUTIONS; INFINITY; REGULARITY; DIRICHLET; DOMAINS;

D O I：

10.1090/proc/14823

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that if Omega is an open bounded domain with smooth and connected boundary, for every p is an element of (1,+infinity) the first Dirichlet eigenvalue of the normalized p-Laplacian is simple in the sense that two positive eigenfunctions are necessarily multiple of each other. We also give a (nonoptimal) lower bound for the eigenvalue in terms of the measure of Omega, and we address the open problem of proving a Faber-Krahn-type inequality with balls as optimal domains.

引用

页码：577 / 590

页数：14

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