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arXiv · 1310.1568

Spectral optimization problems for potentials and measures

Dorin Bucur·Giuseppe Buttazzo·Bozhidar Velichkov
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Abstract

In the present paper we consider spectral optimization problems involving the Schrödinger operator $-Δ+μ$ on $\R^d$, the prototype being the minimization of the $k$ the eigenvalue $λ_k(μ)$. Here $μ$ may be a capacitary measure with prescribed torsional rigidity (like in the Kohler-Jobin problem) or a classical nonnegative potential $V$ which satisfies the integral constraint $\ds \int V^{-p}dx \le m$ with $0<p<1$. We prove the existence of global solutions in $\R^d$ and that the optimal potentials or measures are equal to $+\infty$ outside a compact set.

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Dorin Bucur, Giuseppe Buttazzo, Bozhidar Velichkov. 2013-10-06. Spectral optimization problems for potentials and measures. https://arxiv.org/abs/1310.1568

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