EIGENVALUES FOR A COMBINATION BETWEEN LOCAL AND NONLOCAL p-LAPLACIANS

被引：19
|
作者：
Del Pezzo, Leandro M. [1 ,2 ]
Ferreira, Raul [3 ]
Rossi, Julio D. [1 ,2 ]
机构：
[1] UBA, FCEyN, CONICET, Pab 1,Ciudad Univ C1428BCW, Buenos Aires, DF, Argentina
[2] UBA, FCEyN, Dept Matemat, Pab 1,Ciudad Univ C1428BCW, Buenos Aires, DF, Argentina
[3] Univ Complutense Madrid, Fac CC Quim, Dept Matemat Aplicada, E-28040 Madrid, Spain
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2019年 / 22卷 / 05期
关键词：
fractional calculus; eigenvalues; p-Laplacian; MULTIPLICITY;
D O I：
10.1515/fca-2019-0074
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study the Dirichlet eigenvalue problem -Delta(p)u - Delta(J,p)u = lambda vertical bar u vertical bar(p-2)u in Omega, u = 0 in Omega(c) = R-N\Omega. Here Omega is a bounded domain in R-N, Delta(p)u is the standard local p-Laplacian and Delta(J,p)u is a nonlocal p-homogeneous operator of order zero. We show that the first eigenvalue (that is isolated and simple) satisfies limp(p ->infinity) (lambda(1))(1/p) = Lambda where Lambda can be characterized in terms of the geometry of Omega. We also find that the eigenfunctions converge, u(infinity) = lim(p ->infinity) u(p), and find the limit problem that is satisfied in the limit.
引用
收藏
页码：1414 / 1436
页数：23
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