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

ROSSI, JULIO D.; FERNÁNDEZ BONDER, JULIAN; SPEDALETTI, JUAN F.

ADVANCED NONLINEAR STUDIES

ADVANCED NONLINEAR STUDIES, INC

Año: 2018 vol. 18 p. 323 - 335

1536-1365

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 α). 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 α.