Poincaré inequality and Hajłasz-Sobolev spaces on nested fractals

Katarzyna Pietruska-Pałuba, and Andrzej Stós. "Poincaré inequality and Hajłasz-Sobolev spaces on nested fractals." Studia Mathematica 218.1 (2013): 1-26. <http://eudml.org/doc/285431>.

@article{KatarzynaPietruska2013,
abstract = {Given a nondegenerate harmonic structure, we prove a Poincaré-type inequality for functions in the domain of the Dirichlet form on nested fractals. We then study the Hajłasz-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.},
author = {Katarzyna Pietruska-Pałuba, Andrzej Stós},
journal = {Studia Mathematica},
keywords = {nested fractals; Hajłasz-Sobolev space; Poincaré inequality},
language = {eng},
number = {1},
pages = {1-26},
title = {Poincaré inequality and Hajłasz-Sobolev spaces on nested fractals},
url = {http://eudml.org/doc/285431},
volume = {218},
year = {2013},
}

TY - JOUR
AU - Katarzyna Pietruska-Pałuba
AU - Andrzej Stós
TI - Poincaré inequality and Hajłasz-Sobolev spaces on nested fractals
JO - Studia Mathematica
PY - 2013
VL - 218
IS - 1
SP - 1
EP - 26
AB - Given a nondegenerate harmonic structure, we prove a Poincaré-type inequality for functions in the domain of the Dirichlet form on nested fractals. We then study the Hajłasz-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.
LA - eng
KW - nested fractals; Hajłasz-Sobolev space; Poincaré inequality
UR - http://eudml.org/doc/285431
ER -