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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Ohta, SI. Cheeger Type Sobolev Spaces for Metric Space Targets. Potential Analysis 20, 149–175 (2004). https://doi.org/10.1023/A:1026359313080
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DOI: https://doi.org/10.1023/A:1026359313080