Leray Lions degenerated problem with general growth condition.
Lie symmetries and criticality of semilinear differential systems.
Limits of Nonlinear Dirichlet Problems in varying domains.
Lipschitz Continuous Solutions for Nonlinear Obstacle Problems.
Lipschitz regularity for some asymptotically convex problems
We establish a local Lipschitz regularity result for local minimizers of asymptotically convex variational integrals.
Lipschitz regularity for some asymptotically convex problems*
We establish a local Lipschitz regularity result for local minimizers of asymptotically convex variational integrals.
Local and global estimates for solutions of systems involving the -Laplacian in unbounded domains.
Local boundedness for minimizers of variational integrals under anisotropic nonstandard growth conditions
This paper deals with local boundedness for minimizers of vectorial integrals under anisotropic growth conditions by using De Giorgi’s iterative method. We consider integral functionals with the first part of the integrand satisfying anisotropic growth conditions including a convex nondecreasing function , and with the second part, a convex lower order term or a polyconvex lower order term. Local boundedness of minimizers is derived.
Local Lipschitz continuity of solutions of non-linear elliptic differential-functional equations
The object of this paper is to prove existence and regularity results for non-linear elliptic differential-functional equations of the form over the functions that assume given boundary values ϕ on ∂Ω. The vector field satisfies an ellipticity condition and for a fixed x, F[u](x) denotes a non-linear functional of u. In considering the same problem, Hartman and Stampacchia [Acta Math.115 (1966) 271–310] have obtained existence results in the space of uniformly Lipschitz continuous functions...
Local regularity results for minima of anisotropic functionals and solutions of anisotropic equations.
Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint
This paper is devoted to an analysis of vortex-nucleation for a Ginzburg-Landau functional with discontinuous constraint. This functional has been proposed as a model for vortex-pinning, and usually accounts for the energy resulting from the interface of two superconductors. The critical applied magnetic field for vortex nucleation is estimated in the London singular limit, and as a by-product, results concerning vortex-pinning and boundary conditions on the interface are obtained.
Mathematical modeling of time-harmonic aeroacoustics with a generalized impedance boundary condition
We study the time-harmonic acoustic scattering in a duct in presence of a flow and of a discontinuous impedance boundary condition. Unlike a continuous impedance, a discontinuous one leads to still open modeling questions, as in particular the singularity of the solution at the abrupt transition and the choice of the right unknown to formulate the scattering problem. To address these questions we propose a mathematical approach based on variational formulations set in weighted Sobolev spaces. Considering...
Maximum principles for a class of nonlinear second-order elliptic boundary value problems in divergence form.
Mean curvature and least energy solutions for the critical Neumann problem with weight
In this paper we consider the Neumann problem involving a critical Sobolev exponent. We investigate a combined effect of the coefficient of the critical Sobolev nonlinearity and the mean curvature on the existence and nonexistence of solutions.
Mean curvature properties for -Laplace phase transitions
This paper deals with phase transitions corresponding to an energy which is the sum of a kinetic part of -Laplacian type and a double well potential with suitable growth conditions. We prove that level sets of solutions of possessing a certain decay property satisfy a mean curvature equation in a suitable weak viscosity sense. From this, we show that, if the above level sets approach uniformly a hypersurface, the latter has zero mean curvature.
Metodi variazionali e topologici nello studio delle equazioni di Schrödinger nonlineari agli stati stazionari
In the present paper we survey some recents results concerning existence of semiclassical standing waves solutions for nonlinear Schrödinger equations. Furthermore, from Maxwell's equations we derive a nonlinear Schrödinger equation which represents a model of propagation of an electromagnetic field in optical waveguides.
Minimax characterization of solutions for a semi-linear elliptic equation with lack of compactness
Minimax theorems on manifolds via Ekeland variational principle.
Minimizers of Dirichlet functionals on the -torus and the weak KAM theory
Minimizing Oseen-Frank energy for nematic liquid crystals : algorithms and numerical results