An Embedding Theorem in the Calculus of Variations for Multiple Integrals.
An estimation of the controllability time for single-input systems on compact Lie Groups
Geometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters...
An evolutionary double-well problem
An example in the gradient theory of phase transitions
We prove by giving an example that when the asymptotic behavior of functionals is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case (see [2]) is no longer true in higher dimensions.
An example in the gradient theory of phase transitions
We prove by giving an example that when n ≥ 3 the asymptotic behavior of functionals is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case (see [2]) is no longer true in higher dimensions.
An example of non-convex minimization and an application to Newton's problem of the body of least resistance
An existence and uniqueness result for Hamilton-Jacobi equations in Hilbert spaces
We prove an existence and uniqueness result for a class of Hamilton-Jacobi equations in Hilbert spaces.
An existence and uniqueness result for semilinear equations with Lipschitz nonlinearity.
An existence result for a free boundary problem for the -Laplace operator.
An existence result for a nonconvex variational problem via regularity
Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are not necessarily uniformly convex. In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands nonconvex with respect to the gradient variable. The -dependence, explicitly appearing in the integrands, adds significant technical difficulties in the proof.
An existence result for a nonconvex variational problem via regularity
Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are not necessarily uniformly convex. In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands nonconvex with respect to the gradient variable. The x-dependence, explicitly appearing in the integrands, adds significant technical difficulties in the proof.
An existence result for an interior electromagnetic casting problem
This paper deals with an interior electromagnetic casting (free boundary) problem. We begin by showing that the associated shape optimization problem has a solution which is of class C 2. Then, using the shape derivative and the maximum principle, we give a sufficient condition that the minimum obtained solves our problem.
An existence result for hemivariational inequalities.
An existence result on noncoercive hemivariational inequalities
An existence theorem for a class of nonlinear elliptic optimal control problems
We establish the existence of an optimal ``state-control'' pair for an optimal control problem of Lagrange type, monitored by a nonlinear elliptic partial equation involving nonmonotone nonlinearities.
An existence theorem for a non-regular variational problem.
An Existence Theorem for Class of Non-Coercive Optimization and Variational Problems.
An existence theorem for extended mildly nonlinear complementarity problem in semi-inner product spaces
We prove a result for the existence and uniqueness of the solution for a class of mildly nonlinear complementarity problem in a uniformly convex and strongly smooth Banach space equipped with a semi-inner product. We also get an extension of a nonlinear complementarity problem over an infinite dimensional space. Our last results deal with the existence of a solution of mildly nonlinear complementarity problem in a reflexive Banach space.
An existence theorem for set differential inclusions in a semilinear metric space
An expression of classical dynamics