An elliptic problem with critical exponent and positive Hardy potential.
An equality for the curvature function of a simple and closed curve on the plane.
An existence and localization theorem for the solutions of a Dirichlet problem
We establish an existence theorem for a Dirichlet problem with homogeneous boundary conditions by using a general variational principle of Ricceri.
An existence result for elliptic problems with singular critical growth.
An existence result for nonlinear elliptic problems involving critical Sobolev exponent
An existence theorem for a non-regular variational problem.
An inversion of the obstacle problem and its explicit solution
An L...-Estimate for the gradient of extremals.
An Orlicz-Sobolev space setting for quasilinear elliptic problems.
Antimaximum principle for elliptic problems with weight.
Applications of a max-min principle
Approximation of an elliptic boundary value problem with unilateral constraints
Asymmetric elliptic problems in .
Asymmetric unbounded liquid bridges
Asymptotic and numerical modelling of flows in fractured porous media
This study concerns some asymptotic models used to compute the flow outside and inside fractures in a bidimensional porous medium. The flow is governed by the Darcy law both in the fractures and in the porous matrix with large discontinuities in the permeability tensor. These fractures are supposed to have a small thickness with respect to the macroscopic length scale, so that we can asymptotically reduce them to immersed polygonal fault interfaces and the model finally consists in a coupling between...
Asymptotic behavior of positive solutions of a Dirichlet problem involving supercritical nonlinearities
Let , , and . We study, for , the behavior of positive solutions of the problem in , . In particular, we give a positive answer to an open question formulated in a recent paper of the first author.
Asymptotic properties of ground states of scalar field equations with a vanishing parameter
We study the leading order behaviour of positive solutions of the equation , where , and when is a small parameter. We give a complete characterization of all possible asymptotic regimes as a function of , and . The behavior of solutions depends sensitively on whether is less, equal or bigger than the critical Sobolev exponent . For the solution asymptotically coincides with the solution of the equation in which the last term is absent. For the solution asymptotically coincides...
Asymptotically Linear Elliptic Boundary Value Problems.
Aubry sets and the differentiability of the minimal average action in codimension one
Let (x,u,∇u) be a Lagrangian periodic of period 1 in x1,...,xn,u. We shall study the non self intersecting functions u: RnR minimizing ; non self intersecting means that, if u(x0 + k) + j = u(x0) for some x0∈Rn and (k , j) ∈Zn × Z, then u(x) = u(x + k) + jx. Moser has shown that each of these functions is at finite distance from a plane u = ρx and thus has an average slope ρ; moreover, Senn has proven that it is possible to define the average action of u, which is usually called since...