Optimal Design Problems for the First p-Fractional Eigenvalue with Mixed Boundary Conditions

被引：5

作者：

Fernandez Bonder, Julian ^{[1
,2
]}

Rossi, Julio D. ^{[1
,2
]}

Spedaletti, Juan F. ^{[3
,4
]}

机构：

[1] Univ Buenos Aires, Dept Matemat FCEN, Ciudad Univ,Pabellon 1,C1428EGA,Av Cantilo 2160, Buenos Aires, DF, Argentina

[2] IMAS CONICET, Ciudad Univ,Pabellon 1,C1428EGA,Av Cantilo 2160, Buenos Aires, DF, Argentina

[3] Univ Nacl San Luis, Dept Matemat, Ejercito Andes 950,D5700HHW, San Luis, Argentina

[4] IMASL CONICET, Ejercito Andes 950,D5700HHW, San Luis, Argentina

来源：

ADVANCED NONLINEAR STUDIES | 2018年 / 18卷 / 02期

关键词：

Shape Optimization; Fractional Laplacian; Gamma Convergence; SOBOLEV SPACES; OPTIMIZATION;

D O I：

10.1515/ans-2018-0001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study an optimal shape design problem for the first eigenvalue of the fractional p-Laplacian with mixed boundary conditions. The optimization variable is the set where the Dirichlet condition is imposed (that is restricted to have measure equal to a prescribed quantity alpha). We show existence of an optimal design and analyze the asymptotic behavior when the fractional parameter s converges to 1, and thus obtain asymptotic bounds that are independent of alpha.

引用

页码：323 / 335

页数：13