On some Optimization Problems in Not Necessarily Locally Convex Space
On some properties of Lipschitz mappings of the real line into a normed space.
On some quasiconvex functions with linear growth.
On some recent aspects of stochastic control and their applications.
On some variational inequalities for nonclassical type operators
The purpose of this paper is to make a brief review of results obtained in the theory of variational inequalities for nonclassical operators, namely, of degenerate hyperbolic and variable type.
On subdifferentials of convex functions
On system of generalized vector quasiequilibrium problems with applications.
On the analysis of a viscoplastic contact problem with time dependent Tresca's friction law.
On the analysis of boundary value problems in nonsmooth domains [Book]
On the Approximation of Hausdorff Upper Semi-Continuous Correspondences.
On the approximation of the Signorini problem with friction
On the approximation of the solution of an optimal control problem governed by an elliptic equation
On the Argmin-sets of stochastic processes and their distributional convergence in Fell-type-topologies
Let be the collection of all -optimal solutions for a stochastic process with locally bounded trajectories defined on a topological space. For sequences of such stochastic processes and of nonnegative random variables we give sufficient conditions for the (closed) random sets to converge in distribution with respect to the Fell-topology and to the coarser Missing-topology.
On the best observation of wave and Schrödinger equations in quantum ergodic billiards
This paper is a proceedings version of the ongoing work [20], and has been the object of the talk of the second author at Journées EDP in 2012.In this work we investigate optimal observability properties for wave and Schrödinger equations considered in a bounded open set , with Dirichlet boundary conditions. The observation is done on a subset of Lebesgue measure , where is fixed. We denote by the class of all possible such subsets. Let . We consider first the benchmark problem of maximizing...
On the binding of polarons in a mean-field quantum crystal
We consider a multi-polaron model obtained by coupling the many-body Schrödinger equation for N interacting electrons with the energy functional of a mean-field crystal with a localized defect, obtaining a highly non linear many-body problem. The physical picture is that the electrons constitute a charge defect in an otherwise perfect periodic crystal. A remarkable feature of such a system is the possibility to form a bound state of electrons via their interaction with the polarizable background....
On the boundary element method for the Signorini problem of the Laplacian.
On the composition of quasiconvex functions and the transposition.
On the condition of Λ-convexity in some problems of weak continuity and weak lower semicontinuity
We study the functional , where u=(u₁, ..., uₘ) and each is constant along some subspace of ℝⁿ. We show that if intersections of the ’s satisfy a certain condition then is weakly lower semicontinuous if and only if f is Λ-convex (see Definition 1.1 and Theorem 1.1). We also give a necessary and sufficient condition on to have the equivalence: is weakly continuous if and only if f is Λ-affine.
On the continuity of minimizers for quasilinear functionals
In this paper we establish a continuity result for local minimizers of some quasilinear functionals that satisfy degenerate elliptic bounds. The non-negative function which measures the degree of degeneracy is assumed to be exponentially integrable. The minimizers are shown to have a modulus of continuity controlled by . Our proof adapts ideas developed for solutions of degenerate elliptic equations by J. Onninen, X. Zhong: Continuity of solutions of linear, degenerate elliptic equations, Ann....
On the controllability under constraints on the control for hyperbolic equations.