Publication: Linear non-local diffusion problems in metric measure spaces
Loading...
Official URL
Full text at PDC
Publication Date
2016
Authors
Sastre Gómez, S.
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Cambridge University Press
Citations
Exportar
Abstract
The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ℝN, graphs, manifolds, multi-structures and some fractal sets. For this, we study regularity, compactness, positivity and the spectrum of the stationary non-local operator. We then study the solutions of linear evolution non-local diffusion problems, with emphasis on similarities and differences with the standard heat equation in smooth domains. In particular, we prove weak and strong maximum principles and describe the asymptotic behaviour using spectral methods.