Poincar\'e Inequality and Hajlasz-Sobolev spaces on nested fractals
Functional Analysis
2012-01-18 v1
Abstract
Given a nondegenerate harmonic structure, we prove a Poincar\'e-type inequality for functions in the domain of the Dirichlet form on nested fractals. We then study the Hajlasz-Sobolev spaces on nested fractals. In particular, we describe how the "weak"-type gradient on nested fractals relates to the upper gradient defined in the context of general metric spaces.
Cite
@article{arxiv.1201.3493,
title = {Poincar\'e Inequality and Hajlasz-Sobolev spaces on nested fractals},
author = {Katarzyna Pietruska-Pałuba and Andrzej Stos},
journal= {arXiv preprint arXiv:1201.3493},
year = {2012}
}