arXiv subjects
Publications and source records attributed to L. M. Del Pezzo.
We find interpretation using optimal mass transport theory for eigenvalue problems obtained as limits of the eigenvalue problems for the fractional $p-$Laplacian operators as $p\to +\infty$. We deal both with Dirichlet and Neumann boundary conditions.
In this paper we construct an "Interior Penalty" Discontinuous Galerkin method to approximate the minimizer of a variational problem related to the $p(x)-$Laplacian. The function $p:Ω\to [p_1,p_2]$ is log Hölder continuous and $1<p_1\leq p_2<\infty$. We prove that the minimizers of the discrete functional converge to the solution. We also make some numerical experiments in dimension one to compare this method with the Conforming Galerkin Method, in the case where $p_1$ is close to one. This example is motivated by its applications to image processing.
We study the Sobolev trace constant for functions defined in a bounded domain $Ø$ that vanish in the subset $A.$ We find a formula for the first variation of the Sobolev trace with respect to hole. As a consequence of this formula, we prove that when $Ø$ is a centered ball, the symmetric hole is critical when we consider deformation that preserve volume but is not optimal for some case.