Related papers: Spectral partition problems with volume and inclus…

This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic partial differential equation with nonlinear terms that satisfy global Lipschitz conditions. It is shown…

We consider decaying oscillatory perturbations of periodic Schr\"odinger operators on the half line. More precisely, the perturbations we study satisfy a generalized bounded variation condition at infinity and an $L^p$ decay condition. We…

In this article we study optimization problems ruled by $\alpha$-fractional diffusion operators with volume constraints. By means of penalization techniques we prove existence of solutions. We also show that every solution is locally of…

We consider a shape optimization problem for the persistence threshold of a biological species dispersing in a periodically fragmented environment, the unknown shape corresponding to the portion of the habitat which is favorable to the…

The stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the Einstein metrics. One may consider the modified problem of finding stationary points…

This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…

Consider partitions of an open, bounded domain in $\mathbb{R}^n$. Then an average element of the partition has either its Fraenkel asymmetry or its deviation from the smallest element in the partition bounded away from 0 by a universal…

In this paper we prove the existence of an optimal domain which minimizes the buckling load of a clamped plate among all bounded domains with given measure. Instead of treating this variational problem with a volume constraint, we introduce…

We look for best partitions of the unit interval that minimize certain functionals defined in terms of the eigenvalues of Sturm-Liouville problems. Via \Gamma-convergence theory, we study the asymptotic distribution of the minimizers as the…

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence…

We consider shape optimization problems with internal inclusion constraints, of the form $$\min\big\{J(\Omega)\ :\ \Dr\subset\Omega\subset\R^d,\ |\Omega|=m\big\},$$ where the set $\Dr$ is fixed, possibly unbounded, and $J$ depends on…

We study a free boundary problem arising from the theory of thermal insulation. The outstanding feature of this set optimization problem is that the boundary of the set being optimized is not a level surface of a harmonic function, but…

We study the singular set of free interface in an optimal partition problem for the Dirichlet eigenvalues. We prove that its upper $(n-2)$-dimensional Minkowski content, and consequently, its $(n-2)$-dimensional Hausdorff measure are…

A long-standing open problem in harmonic analysis is: given a non-negative measure $\mu$ on $\mathbb R$, find the infimal width of frequencies needed to approximate any function in $L^2(\mu)$. We consider this problem in the "perturbative…

We study the optimization of Steklov eigenvalues with respect to a boundary density function $\rho$ on a bounded Lipschitz domain $\Omega \subset \mathbb{R}^N$. We investigate the minimization and maximization of $\lambda_k(\rho)$, the…

Let M be an oriented three-dimensional Riemannian manifold. We define a notion of vorticity of local sections of the bundle SO(M) --> M of all its positively oriented orthonormal tangent frames. When M is a space form, we relate the concept…

We consider spectral minimal partitions. Continuing work of the the present authors about problems for planar domains, [23], we focus on the sphere and obtain a sharp result for 3-partitions which is related to questions from harmonic…

We analyze a convex stochastic optimization problem where the state is assumed to belong to the Bochner space of essentially bounded random variables with images in a reflexive and separable Banach space. For this problem, we obtain…

We study the minimization of a spectral functional made as the sum of the first eigenvalue of the Dirichlet Laplacian and the relative strength of a Riesz-type interaction functional. We show that when the Riesz repulsion strength is below…

We consider a stochastic functional differential equation with an arbitrary Lipschitz diffusion coefficient depending on the past. The drift part contains a term with superlinear growth and satisfying a dissipativity condition. We prove…