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.
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Koskela, P., Shanmugalingam, N. & Tyson, J.T. Dirichlet Forms, Poincaré Inequalities, and the Sobolev Spaces of Korevaar and Schoen. Potential Analysis 21, 241–262 (2004). https://doi.org/10.1023/B:POTA.0000033331.88514.6e
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DOI: https://doi.org/10.1023/B:POTA.0000033331.88514.6e