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arXiv · 1702.04315

Optimal design problems for the first $p-$fractional eigenvalue with mixed boundary conditions

Julian Fernandez Bonder·Julio D. Rossi·Juan F. Spedaletti
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Abstract

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 $\alpha$.

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Julian Fernandez Bonder, Julio D. Rossi, Juan F. Spedaletti. 2017-02-14. Optimal design problems for the first $p-$fractional eigenvalue with mixed boundary conditions. https://arxiv.org/abs/1702.04315

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