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.
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页码：323 / 335
页数：13
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