We prove local embeddings of Sobolev and Morrey type for Dirichlet forms on spaces of homogeneous type. Our results apply to some general classes of selfadjoint subelliptic operators as well as to Dirichlet operators on certain self-similar fractals, like the Sierpinski gasket. We also define intrinsic BV spaces and perimeters and prove related isoperimetric inequalities.
Si provano risultati di immersione locale del tipo Sobolev e Morrey per forme di Dirichlet su spazi di tipo omogeneo. I risultati si applicano a certe classi generali di operatori subellitici e a operatori di Dirichlet su certi frattali come il «Sierpinski gasket». Si definiscono inoltre spazi BV e perimetri intrinseci e si ottengono per essi diseguaglianze isoperimetriche.
@article{RLIN_1995_9_6_1_37_0,
author = {Marco Biroli and Umberto Mosco},
title = {Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
volume = {6},
year = {1995},
pages = {37-44},
zbl = {0837.31006},
mrnumber = {1340280},
language = {en},
url = {http://dml.mathdoc.fr/item/RLIN_1995_9_6_1_37_0}
}
Biroli, Marco; Mosco, Umberto. Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 6 (1995) pp. 37-44. http://gdmltest.u-ga.fr/item/RLIN_1995_9_6_1_37_0/
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