Poincar\'e Inequality and Hajlasz-Sobolev spaces on nested fractals

Autor:	Pietruska-Pałuba, Katarzyna, Stos, Andrzej
Rok vydání:	2012
Předmět:	Mathematics - Functional Analysis
Druh dokumentu:	Working Paper
Popis:	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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1201.3493 Zobrazit plný text záznamu View this record from Arxiv