Related papers: Stability in shape optimization with second variat…
In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation…
For $\Omega$ varying among open bounded sets in ${\mathbb R} ^n$, we consider shape functionals $J (\Omega)$ defined as the infimum over a Sobolev space of an integral energy of the kind $\int _\Omega[ f (\nabla u) + g (u) ]$, under…
Optimal second-order regularity in the space variables is established for solutions to Cauchy-Dirichlet problems for nonlinear parabolic equations and systems of $p$-Laplacian type, with square-integrable right-hand sides and initial data…
In the present article, we discuss some aspects of the local stability analysis for a class of abstract functional differential equations. This is done under smoothness assumptions which are often satisfied in the presence of a…
This paper is concerned with the structural stability of spherical horizons. By this we mean stability with respect to variations of the second member of the corresponding differential equations, corresponding to the inclusion of the…
This paper is concerned with the study of linear geometric rigidity of shallow thin domains under zero Dirichlet boundary conditions on the displacement field on the thin edge of the domain. A shallow thin domain is a thin domain that has…
We prove the convergence of the fixed-point (also called thresholding) algorithm in three optimal control problems under large volume constraints. This algorithm was introduced by C\'ea, Gioan and Michel, and is of constant use in the…
This paper is devoted to the study of tilt stability in finite dimensional optimization via the approach of using the subgradient graphical derivative. We establish a new characterization of tilt-stable local minimizers for a broad class of…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
A second-order regularity theory is developed for solutions to a class of quasilinear elliptic equations in divergence form, including the $p$-Laplace equation, with merely square-integrable right-hand side. Our results amount to the…
We consider the question of quantitative stability of minimisers for a well-known variational problem for which the infimum of the energy is not achieved in the classical sense, namely for the Dirichlet energy of degree $1$ maps from closed…
We study the problem of minimizing the second Dirichlet eigenvalue for the Laplacian operator among sets of given perimeter. In two dimensions, we prove that the optimum exists, is convex, regular, and its boundary contains exactly two…
Using techniques from harmonic analysis, we derive several sharp stability estimates for the second order Heisenberg Uncertainty Principle. We also present the explicit lower and upper bounds for the sharp stability constants and compute…
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…
It is known that the torsional rigidity for a punctured ball, with the puncture having the shape of a ball, is minimum when the balls are concentric and the first eigenvalue for the Dirichlet Laplacian for such domains is also a maximum in…
This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of…
We study the stability of $p$-area minimizing surfaces in the Heisenberg group under perturbations of the weight function and the drift vector field in generalized least gradient problems of the form \[ \inf_{w\in BV_0(\Omega)} \int_\Omega…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
We consider nearly-integrable Hamiltonian systems defined over a non-resonant domain. In the neighborhood of resonances, we use Nekhoroshev-like estimates to provide effective stability bounds for the action variables over long time. The…
We consider a shape optimization problem related to the persistence threshold for a biological species, the unknown shape corresponding to the zone of the habitat which is favorable to the population. Analytically, this translates in the…