Poincaré inequality and Hajłasz-Sobolev spaces on nested fractals
Katarzyna Pietruska-Pałuba ; Andrzej Stós
Studia Mathematica, Tome 215 (2013), p. 1-26 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:285431 
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm218-1-1,
     author = {Katarzyna Pietruska-Pa\l uba and Andrzej St\'os},
     title = {Poincar\'e inequality and Haj\l asz-Sobolev spaces on nested fractals},
     journal = {Studia Mathematica},
     volume = {215},
     year = {2013},
     pages = {1-26},
     zbl = {1300.46030},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm218-1-1}
}

Katarzyna Pietruska-Pałuba; Andrzej Stós. Poincaré inequality and Hajłasz-Sobolev spaces on nested fractals. Studia Mathematica, Tome 215 (2013) pp. 1-26. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm218-1-1/