Asymptotics for quasilinear obstacle problems in bad domains

We study two obstacle problems involving the p-Laplace operator in domains with n-th pre-fractal and fractal boundary. We perform asymptotic analysis for $p o infty$ and $n o infty$

Limit of p-Laplacian Obstacle problems

In this paper we study asymptotic behavior of solutions of obstacle problems for $p-$Laplacians as $p\to \infty.$ For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of whole family of the solutions of obstacle problems either for data $f$ that change sign in $\Omega$ or for data $f$ (that do not change sign in $\Omega$) possibly vanishing in a set of positive measure

Weighted Estimates on fractal domains

The aim of the paper is to establish estimates in weighted Sobolev spaces for the solutions of the Dirichlet problems on snowflake domains, as well as uniform estimates for the solutions of the Dirichlet problems on pre-fractal approximating domains

Reinforcement problems for variational inequalities on fractal sets

The aim of this paper is to study reinforcement problems for variational inequalities of the obstacle type on fractal sets

Delayed and rushed motions through time change

We introduce a definition of delayed and rushed processes in terms of lifetimes of base processes and time-changed base processes. Then, we consider time changes given by subordinators and their inverse processes. Our analysis shows that, quite surprisingly, time-changing with inverse subordinators does not necessarily imply delay of the base process. Moreover, time-changing with subordinators does not necessarily imply rushed base process.Comment: to appear on ALEA - Latin American Journal of Probability and Mathematical Statistic

Eikonal equations on the Sierpinski gasket

We study the eikonal equation on the Sierpinski gasket in the spirit of the construction of the Laplacian in Kigami [8]: we consider graph eikonal equations on the prefractals and we show that the solutions of these problems converge to a function defined on the fractal set. We characterize this limit function as the unique metric viscosity solution to the eikonal equation on the Sierpinski gasket according to the definition introduced in [3]

La geografía como sistema

Fil: Capitanelli, Ricardo