Concavity properties of solutions to Robin problems

被引：0

作者：

Crasta, Graziano ^{[1
]}

Fragala, Ilaria ^{[2
]}

机构：

[1] Sapienza Univ Roma, Dipartimento Matemat G Castelnuovo, Ple A Moro 5, I-00185 Rome, Italy

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

来源：

CAMBRIDGE JOURNAL OF MATHEMATICS | 2021年 / 9卷 / 01期

关键词：

Robin boundary conditions; eigenfunctions; torsion function; concavity; CONVEX SOLUTIONS; ASYMPTOTIC-BEHAVIOR; ELLIPTIC-EQUATIONS; BOUNDARY; EIGENFUNCTIONS; EIGENVALUES; MINKOWSKI;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the Robin ground state and the Robin torsion function are respectively log-concave and 1/2-concave on an uniformly convex domain Omega subset of R-N of class (Cm), with [m - N/2] >= 4, provided the Robin parameter exceeds a critical threshold. Such threshold depends on N, m, and on the geometry of Omega, precisely on the diameter and on the boundary curvatures up to order m.

引用

页码：177 / 212

页数：36

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