Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials.
Existence of a closed geodesic on -convex sets
Extremal functions for the Trudinger-Moser inequality in 2 dimensions.
Holes and obstacles
Inégalités variationnelles non convexes
Dans cet article nous proposons différents algorithmes pour résoudre une nouvelle classe de problèmes variationels non convexes. Cette classe généralise plusieurs types d’inégalités variationnelles (Cho et al. (2000), Noor (1992), Zeng (1998), Stampacchia (1964)) du cas convexe au cas non convexe. La sensibilité de cette classe de problèmes variationnels non convexes a été aussi étudiée.
Inégalités variationnelles non convexes
Dans cet article nous proposons différents algorithmes pour résoudre une nouvelle classe de problèmes variationels non convexes. Cette classe généralise plusieurs types d'inégalités variationnelles (Cho et al. (2000), Noor (1992), Zeng (1998), Stampacchia (1964)) du cas convexe au cas non convexe. La sensibilité de cette classe de problèmes variationnels non convexes a été aussi étudiée.
Iterative schemes to solve nonconvex variational problems.
Minimization problems with lack of compactness
Multiple solutions for a singular semilinear elliptic problems with critical exponent and symmetries.
On Bilevel Variational Inequalities Arising in the Analysis of Improper Optimization Problems
On the mountain pass lemma
Optimal control of variational inequality with applications to axisymmetric shells
The optimal control problem of variational inequality with applications to axisymmetric shells is discussed. First an existence result for the solution of the optimal control problem is given. Next is presented the formulation of first order necessary conditionas of optimality for the control problem governed by a variational inequality with its coefficients as control variables.
Optimal Regularity Theorems for Variational Problems with Obstacles.
Optimization problems on complete Riemannian manifolds
Perturbations of Critical Values in Nonsmooth Critical Point Theory
* Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993). ** Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993).The perturbation of critical values for continuous functionals is studied. An application to eigenvalue problems for variational inequalities is provided.
Piecewise solutions of evolutionary variational inequalities. Application to double-layered dynamics modelling of equilibrium problems.
Prékopa–Leindler type inequalities on Riemannian manifolds, Jacobi fields, and optimal transport
We investigate Prékopa-Leindler type inequalities on a Riemannian manifold equipped with a measure with density where the potential and the Ricci curvature satisfy for all , with some . As in our earlier work [14], the argument uses optimal mass transport on , but here, with a special emphasis on its connection with Jacobi fields. A key role will be played by the differential equation satisfied by the determinant of a matrix of Jacobi fields. We also present applications of the method...
Quasistatic frictional problems for elastic and viscoelastic materials
We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution variational...
Regularity for Signorini's Problem in linear eleasticity.
Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type
We prove the hypoellipticity for systems of Hörmander type with constant coefficients in Carnot groups of step 2. This result is used to implement blow-up methods and prove partial regularity for local minimizers of non-convex functionals, and for solutions of non-linear systems which appear in the study of non-isotropic metric structures with scalings. We also establish estimates of the Hausdorff dimension of the singular set.