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math.AP2020
Regularity of the optimal sets for the second Dirichlet eigenvalue
Dario Mazzoleni, Baptiste Trey, Bozhidar Velichkov
This paper is dedicated to the regularity of the optimal sets for the second eigenvalue of the Dirichlet Laplacian. Precisely, we prove that if the set minimizes the functional…
math.AP2020
Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form
Baptiste Trey
In this paper we consider minimizers of the functional \begin{equation*} \min \big\{ λ_1(Ω)+\cdots+λ_k(Ω) + Λ|Ω|, \ : \ Ω\subset D \text{ open} \big\} \end{equation*} where $D\subs…