Variational methods and linearization tools towards the spectral analysis of the -Laplacian, especially for the Fredholm alternative.
Variational methods for a resonant problem with the -Laplacian in .
Variational methods in mathematical theory of viscoelasticity
Variational methods in nonlinear problems
Variational methods of solving linear and nonlinear boundary value problems
Variational models for quasi-static non-Newtonian fluids
Variational particle schemes for the porous medium equation and for the system of isentropic Euler equations
Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these variational characterizations instead of the partial differential equations themselves, we obtain new schemes with remarkable stability properties. We show that they capture successfully the nonlinear features of the flows, such as shocks and rarefaction waves for...
Variational principle for nonlinear Schrödinger equation with high nonlinearity.
Variational problems in domains with cusp points
The finite element analysis of linear elliptic problems in two-dimensional domains with cusp points (turning points) is presented. This analysis needs on one side a generalization of results concerning the existence and uniqueness of the solution of a constinuous elliptic variational problem in a domain the boundary of which is Lipschitz continuous and on the other side a presentation of a new finite element interpolation theorem and other new devices.
Variational problems on classes of rearrangements and multiple configurations for steady vortices
Variational problems with free boundaries for the fractional Laplacian
We discuss properties (optimal regularity, nondegeneracy, smoothness of the free boundary etc.) of a variational interface problem involving the fractional Laplacian; due to the nonlocality of the Dirichlet problem, the task is nontrivial. This difficulty is bypassed by an extension formula, discovered by the first author and Silvestre, which reduces the study to that of a codimension 2 (degenerate) free boundary.
Variational problems with non-constant gradient constraints.
Variational problems with pointwise constraints on the derivatives.
Variational Reduction for the Transport Equation in a Multiple Branching Plants Growth Model
Plant growth depends essentially on nutrients coming from the roots and metabolites produced by the plant. Appearance of new branches is determined by concentrations of certain plant hormones. The most important of them are Auxin and Cytokinin. Auxin is produced in the growing, Cytokinin in either roots or in growing parts. Many dynamical models of this phenomena have been studied in [1]. In [5], the authors deal with one branch model. In this work,...
Variational-hemivariational inequalities in nonlinear elasticity. The coercive case
Existence of a solution of the problem of nonlinear elasticity with non-classical boundary conditions, when the relationship between the corresponding dual quantities is given in terms of a nonmonotone and generally multivalued relation. The mathematical formulation leads to a problem of non-smooth and nonconvex optimization, and in its weak form to hemivariational inequalities and to the determination of the so called substationary points of the given potential.
Varietà generiche rispetto a sistemi differenziali
Variétés inertielles dans le cas non auto-adjoint. Applications aux variétés lentes
Various kinds of sensitive singular perturbations
We consider variational problems of P. D. E. depending on a small parameter when the limit process implies vanishing of the higher order terms. The perturbation problem is said to be sensitive when the energy space of the limit problem is out of the distribution space, so that the limit problem is out of classical theory of P. D. E. We present here a review of the subject, including abstract convergence theorems and two very different model problems (the second one is presented for the first...
Various representations for the system of hyperbolic equations with singular coefficients.
Various representations for the system of non-model hyperbolic equations with regular coefficients.