Cheeger Type Sobolev Spaces for Metric Space Targets |
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Authors: | Ohta Shin-Ichi |
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Institution: | (1) Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan (e-mail |
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Abstract: | In this paper, we consider the natural generalization of Cheeger type Sobolev spaces to maps into a metric space. We solve Dirichlet problem for CAT(0)-space targets, and obtain some results about the relation between Cheeger type Sobolev spaces for maps into a Banach space and those for maps into a subset of that Banach space. We also prove the minimality of upper pointwise Lipschitz constant functions for locally Lipschitz maps into an Alexandrov space of curvature bounded above. |
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Keywords: | Sobolev space metric space Dirichlet problem |
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