An optimization problem for the first eigenvalue of the p-fractional Laplacian

被引：13
|
作者：
Del Pezzo, Leandro [1 ]
Fernandez Bonder, Julian [2 ,3 ]
Lopez Rios, Luis [2 ,3 ]
机构：
[1] Univ Torcuato Tella, Dept Matemat & Estadist, Av Figueroa Alcorta 7350 C1428BCW, Buenos Aires, DF, Argentina
[2] Univ Buenos Aires, FCEN, Dept Matemat, Ciudad Univ,Pabellon 1 C1428EGA Av Cantilo 2160, Buenos Aires, DF, Argentina
[3] Consejo Nacl Invest Cient & Tecn, IMAS, Ciudad Univ,Pabellon 1 C1428EGA Av Cantilo 2160, Buenos Aires, DF, Argentina
来源：
MATHEMATISCHE NACHRICHTEN | 2018年 / 291卷 / 04期
关键词：
Optimization; fractional laplacian; nonlinear eigenvalues;
D O I：
10.1002/mana.201600110
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we analyze an eigenvalue problem related to the nonlocal p-Laplace operator plus a potential. After reviewing some elementary properties of the first eigenvalue of these operators (existence, positivity of associated eigenfunctions, simplicity and isolation) we investigate the dependence of the first eigenvalue on the potential function and establish the existence of some optimal potentials in some admissible classes.
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页码：632 / 651
页数：20
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