Raffaela Capitanelli

On the Laplacean transfer across fractal mixtures

Laplacean transport across and towards irregular interfaces have been used to model many phenomena in nature and technology. The peculiar aspect is that these phenomena take place in domains with small bulk and large interfaces in order to produce rapid and efficient transport. In this paper we perform the asymptotic homogenization analysis of Robin problems in domains with a fractal boundary.

Mixed Dirichlet-Robin Problems in Irregular Domains

We study mixed Dirichlet-Robin problems for the Laplacian in irregular domains. Our interest in these problems is motivated by some recent applications in physics, electrochemistry, heterogeneous catalysis and physiology. [ DOI : 10.1685 / CSC06035] About DOI

Transfer Across Scale Irregular Domains

We prove existence, uniqueness and regularity results for a mixed DirichletRobin problem on scale irregular domains. These results are comparable with the numerical study on the Laplacian transfer across fractal surfaces.

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. §

Dynamical Quasi-Filling Fractal Layers

The aim of this paper is to investigate second order transmission problems across quasi-filling dynamical layers from the point of view of the variational convergence of energy forms. We prove that the solution to the second order transmission problem across a Koch-type curve is the limit of the solutions to suitable second order transmission problems across polygonal curves.

Regularity results for p-Laplacians in pre-fractal domains

Abstract We study obstacle problems involving p-Laplace-type operators in non-convex polygons. We establish regularity results in terms of weighted Sobolev spaces. As applications, we obtain estimates for the FEM approximation for obstacle problems in pre-fractal Koch Islands.

Harnack Inequality for p-Laplacians on Metric Fractals

By using the approach of the metric fractals, we prove a Harnack inequality for non-negative local supersolutions of p-Laplacians — associated to p-Lagrangians — on metric fractals whose homogeneous dimension is less than p.