We consider spectral optimization problems of the form $$minBig{lambda_1(Omega;D): Omegasubset D, |Omega|=1Big},$$ where $D$ is a given subset of the Euclidean space $R^d$. Here $lambda_1(Omega;D)$ is the first eigenvalue of the Laplace operator $-Delta$ with Dirichlet conditions on $partialOmegacap D$ and Neumann or Robin conditions on $partialOmegacappartial D$. This reminds the classical drop problems, where the first eigenvalue replaces the perimeter functional. We prove an existence result for general shape cost functionals and we show some qualitative properties of the optimal domains
In this thesis, we study the existence and the regularity of optimal shapes for some spectral optimi...
We study the optimization of the positive principal eigenvalue of an indefinite weighted problem, as...
We study the minimization of a spectral functional made as the sum of the first eigenvalue of the Di...
We present some open problems and obtain some partial results for spectral optimization problems inv...
We establish the existence and find some qualitative properties of open sets that minimize functiona...
In this paper we study the regularity of the optimal sets for the shape optimization problem min{λ1(...
International audienceIn this paper, we review known results and open problems on the question of {\...
In this paper we prove that the shape optimization problem {λk (Ω) : Ω ⊂ ℝd, Ω open, P(Ω) = 1, |Ω| &...
We study the optimal sets (Formula presented.) for spectral functionals of the form (Formula present...
For $\Omega \subset \mathbb{R}^n$, a convex and bounded domain, we study the spectrum of $-\Delta_\O...
„Shape optimization and spectral theory” is a survey book aiming to give an overview of recent resul...
We prove the existence and regularity of optimal shapes for the problem min{P(Ω)+G(Ω):Ω⊂D,|Ω|=m}, w...
International audienceWe consider a spectral optimal design problem involving the Neumann traces of ...
In this thesis, we study the existence and the regularity of optimal shapes for some spectral optimi...
We study the optimization of the positive principal eigenvalue of an indefinite weighted problem, as...
We study the minimization of a spectral functional made as the sum of the first eigenvalue of the Di...
We present some open problems and obtain some partial results for spectral optimization problems inv...
We establish the existence and find some qualitative properties of open sets that minimize functiona...
In this paper we study the regularity of the optimal sets for the shape optimization problem min{λ1(...
International audienceIn this paper, we review known results and open problems on the question of {\...
In this paper we prove that the shape optimization problem {λk (Ω) : Ω ⊂ ℝd, Ω open, P(Ω) = 1, |Ω| &...
We study the optimal sets (Formula presented.) for spectral functionals of the form (Formula present...
For $\Omega \subset \mathbb{R}^n$, a convex and bounded domain, we study the spectrum of $-\Delta_\O...
„Shape optimization and spectral theory” is a survey book aiming to give an overview of recent resul...
We prove the existence and regularity of optimal shapes for the problem min{P(Ω)+G(Ω):Ω⊂D,|Ω|=m}, w...
International audienceWe consider a spectral optimal design problem involving the Neumann traces of ...
In this thesis, we study the existence and the regularity of optimal shapes for some spectral optimi...
We study the optimization of the positive principal eigenvalue of an indefinite weighted problem, as...
We study the minimization of a spectral functional made as the sum of the first eigenvalue of the Di...