Julian Fernandez Bonder, Julio D. Rossi, Juan F. Spedaletti
Published 2017-02-14Version 1
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 than a prescribed quantity, $\alpha$). We show existence of an optimal design and analyze the asymptotic behavior when the fractional parameter $s\uparrow 1$ obtaining asymptotic bounds that are independent of $\alpha$.
Comments: 16 pages, submitted
An optimization problem for the first eigenvalue of the $p-$fractional laplacian
On the strict monotonicity of the first eigenvalue of the $p$-Laplacian on annuli
Sharp lower bound for the first eigenvalue of the Weighted $p$-Laplacian
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