Poincaré Inequality and Hajlasz-Sobolev spaces on nested fractals

Details Poincaré Inequality and Hajlasz-Sobolev spaces on nested fractals Poincaré Inequality and Hajlasz-Sobolev spaces on nested fractals

2012-01-17

arxiv.org/abs/1201.3493v1

Mathematics

Functional Analysis

Scientific paper

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.

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