Some inverse mapping theorems
Some iterative methods for solving equilibrium problems and optimization problems.
Some Krasnonsel'skiĭ-Mann algorithms and the multiple-set split feasibility problem. (Some Krasnosel'skiĭ-Mann algorithms and the multiple-set split feasibility problem.)
Some Liouville theorems for PDE problems in periodic media
Liouville problems in periodic media (i.e. the study of properties of global solutions to PDE) arise both in homogenization and dynamical systems. We discuss some recent results for minimal surfaces and free boundaries.
Some maximal elements' theorems in -spaces.
Some Minimax Theorems.
Some new deterministic and random variational inequalities and their applications.
Some new existence, sensitivity and stability results for the nonlinear complementarity problem
In this work we study the nonlinear complementarity problem on the nonnegative orthant. This is done by approximating its equivalent variational-inequality-formulation by a sequence of variational inequalities with nested compact domains. This approach yields simultaneously existence, sensitivity, and stability results. By introducing new classes of functions and a suitable metric for performing the approximation, we provide bounds for the asymptotic set of the solution set and coercive existence...
Some new problems in spectral optimization
We present some new problems in spectral optimization. The first one consists in determining the best domain for the Dirichlet energy (or for the first eigenvalue) of the metric Laplacian, and we consider in particular Riemannian or Finsler manifolds, Carnot-Carathéodory spaces, Gaussian spaces. The second one deals with the optimal shape of a graph when the minimization cost is of spectral type. The third one is the optimization problem for a Schrödinger potential in suitable classes.
Some numerical methods for the study of the convexity notions arising in the calculus of variations
Some optimal control applications of real-analytic stratifications and desingularization
Some optimal control problems of multistate equations appearing in fluid mechanics
Some Properties of Convex Sets Related to Fixed Points Theorems*.
Some regularity results for a family of variational inequalities
Some regularity results for minimal crystals
We introduce an intrinsic notion of perimeter for subsets of a general Minkowski space ( a finite dimensional Banach space in which the norm is not required to be even). We prove that this notion of perimeter is equivalent to the usual definition of surface energy for crystals and we study the regularity properties of the minimizers and the quasi-minimizers of perimeter. In the two-dimensional case we obtain optimal regularity results: apart from a singular set (which is -negligible and is empty...
Some regularity results for minimal crystals
We introduce an intrinsic notion of perimeter for subsets of a general Minkowski space (i.e. a finite dimensional Banach space in which the norm is not required to be even). We prove that this notion of perimeter is equivalent to the usual definition of surface energy for crystals and we study the regularity properties of the minimizers and the quasi-minimizers of perimeter. In the two-dimensional case we obtain optimal regularity results: apart from a singular set (which is -negligible and is...
Some relations among volume, intrinsic perimeter and one-dimensional restrictions of functions in Carnot groups
Let be a -step Carnot group. The first aim of this paper is to show an interplay between volume and -perimeter, using one-dimensional horizontal slicing. What we prove is a kind of Fubini theorem for -regular submanifolds of codimension one. We then give some applications of this result: slicing of functions, integral geometric formulae for volume and -perimeter and, making use of a suitable notion of convexity, called-convexity, we state a Cauchy type formula for -convex sets. Finally,...
Some relations between variational-like inequalities and efficient solutions of certain nonsmooth optimization problems.
Some remarks about a notion of rearrangement
Some remarks about strictly pseudoconvex functions with respect to the Clarke-Rockafellar subdifferential.