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 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.
Some remarks about the density of smooth functions in weighted Sobolev spaces.
Some remarks and applications of an extension of a lemma of Ky Fan
Some remarks on existence results for optimal boundary control problems
An optimal control problem when controls act on the boundary can also be understood as a variational principle under differential constraints and no restrictions on boundary and/or initial values. From this perspective, some existence theorems can be proved when cost functionals depend on the gradient of the state. We treat the case of elliptic and non-elliptic second order state laws only in the two-dimensional situation. Our results are based on deep facts about gradient Young measures.
Some remarks on existence results for optimal boundary control problems
An optimal control problem when controls act on the boundary can also be understood as a variational principle under differential constraints and no restrictions on boundary and/or initial values. From this perspective, some existence theorems can be proved when cost functionals depend on the gradient of the state. We treat the case of elliptic and non-elliptic second order state laws only in the two-dimensional situation. Our results are based on deep facts about gradient Young measures.
Some remarks on nonlinear functionals