Related papers: A maximum principle in spectral optimization probl…

We generalize the Maximum Principle for free end point optimal control problems involving sweeping systems derived in [9] to cover the case where the end point is constrained to take values in a certain set. As in [9], an ingenious smooth…

We address extremum problems for spectral quantities associated with operators of the form $\Delta^2-\tau\Delta$ with Dirichlet boundary conditions, for non-negative values of $\tau$. The focus is on two shape optimisation problems:…

In this paper, we discuss a class of spectral partition problems with a measure constraint, for partitions of a given bounded connected open set. We establish the existence of an optimal open partition, showing that the corresponding…

We consider uniformly elliptic operators with Dirichlet or Neumann homogeneous boundary conditions on a domain $\Omega $ in ${\mathbb{R}}^N$. We consider deformations $\phi (\Omega)$ of $\Omega $ obtained by means of a locally Lipschitz…

This paper classifies the set of supersolutions of a general class of periodic-parabolic problems in the presence of a positive supersolution. From this result we characterize the positivity of the underlying resolvent operator through the…

We prove extensions of the estimates of Aleksandrov and Bakel$'$man for linear elliptic operators in Euclidean space $\Bbb{R}^{\it n}$ to inhomogeneous terms in $L^q$ spaces for $q < n$. Our estimates depend on restrictions on the…

We study a shape optimization problem associated with the first eigenvalue of a nonlinear spectral problem involving a mixed operator ($p-$Laplacian and Laplacian) with a constraint on the volume. First, we prove the existence of a…

In this paper we prove a strong maximum principle for certain parabolic systems of equations. In particular, our methods place no restriction on the regularity of the boundary of the convex set in which the system takes its values, and…

We investigate optimal control problems with $L^0$ constraints, which restrict the measure of the support of the controls. We prove necessary optimality conditions of Pontryagin maximum principle type. Here, a special control perturbation…

The paper is concerned with the principal eigenvalue of some linear elliptic operators with drift in two dimensional space. We provide a refined description of the asymptotic behavior for the principal eigenvalue as the drift rate…

Let $\Omega\subset\mathbb{R}^d$ be any open set. We consider solutions of $H\psi_\lambda=\lambda \psi_\lambda$, $\lambda\in\mathbb{C}$, where $H$ is an $m$th order complex constant-coefficient elliptic partial differential operator. We…

In this note, we first try to prove a uniform lower bound of nodal volume in elliptic homogenization setting. This lower bound is far from optimal. But, we can prove a constant lower bound in dimension two. Motivated by the proof, we extend…

We consider general second order uniformly elliptic operators subject to homogeneous boundary conditions on open sets $\phi (\Omega)$ parametrized by Lipschitz homeomorphisms $\phi $ defined on a fixed reference domain $\Omega$. Given two…

In this paper, we are interested in the analysis of a well-known free boundary/shape optimization problem motivated by some issues arising in population dynamics. The question is to determine optimal spatial arrangements of favorable and…

We prove a maximum principle of optimal control of stochastic delay equations on infinite horizon. We establish first and second sufficient stochastic maximum principles as well as necessary conditions for that problem. We illustrate our…

This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…

We revisit the classical theory of linear second-order uniformly elliptic equations in divergence form whose solutions have H\"older continuous gradients, and prove versions of the generalized maximum principle, the $C^{1,\alpha}$-estimate,…

Preservation of the maximum principle is studied for the combination of the linear finite element method in space and the $\theta$-method in time for solving time dependent anisotropic diffusion problems. It is shown that the numerical…

We study the spectral behavior of higher order elliptic operators upon domain perturbation. We prove general spectral stability results for Dirichlet, Neumann and intermediate boundary conditions. Moreover, we consider the case of the…

This is the final part of a series of papers where we study perturbations of divergence form second order elliptic operators $-\operatorname{div} A \nabla$ by first and zero order terms, whose complex coefficients lie in critical spaces,…