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Dirichlet Forms,Poincaré Inequalities,and the Sobolev Spaces of Korevaar and Schoen |
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| Authors: | Koskela Pekka Shanmugalingam Nageswari Tyson Jeremy T |
| Institution: | (1) Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), FIN-40014 Jyväskylä, Finland (e-mail;(2) Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, Cincinnati, OH, 45221-0025, U.S.A. (e-mail;(3) Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL, 61801, U.S.A. (e-mail |
| Abstract: | We answer a question of Jost on the validity of Poincaré inequalities for metric space-valued functions in a Dirichlet domain. We also investigate the relationship between Dirichlet domains and the Sobolev-type spaces introduced by Korevaar and Schoen. |
| Keywords: | Dirichlet form Sobolev space Lipschitz function Poincaré inequality Cheeger's differentiation theorem doubling measure |
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