5 papers
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…
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…
Lipschitz continuity of the eigenfunctions on optimal sets for functionals with variable coefficients
Baptiste Trey
This paper is dedicated to the spectral optimization problem \begin{equation*} \min \big\{ λ_1(Ω)+\cdots+λ_k(Ω) + Λ|Ω| \ : \ Ω\subset D \text{ quasi-open} \big\} \end{equation*} wh…
Free boundary regularity for a multiphase shape optimization problem
Luca Spolaor, Baptiste Trey, Bozhidar Velichkov
In this paper we prove a regularity result in dimension two for almost-minimizers of the constrained one-phase Alt-Caffarelli and the two-phase Alt-Caffarelli-Friedman fu…
Existence and Regularity of Optimal Shapes for Elliptic Operators with Drift
Emmanuel Russ, Baptiste Trey, Bozhidar Velichkov
This paper is devoted to the study of shape optimization problems for the first eigenvalue of the elliptic operator with drift L = --+V (x)\cdot \nabla with Dirichlet boundary c…