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.
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页码：177 / 212
页数：36
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