Regularity of Harmonic Functions in Cheeger-Type Sobolev Spaces |
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| Authors: | Ohta Shin-Ichi |
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| Institution: | (1) Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606-8502, Japan |
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| Abstract: | We give a geometric approach to the study of the regularity of harmonic functions in Cheeger-type Sobolev spaces, and prove the Hölder continuity of such functions. In the proof, we give a definition of an upper curvature bound of the unit sphere of a Banach space, which seems to be of independent interest. |
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| Keywords: | harmonic functions Hö lder continuity Cheeger-type energy form Banach spaces curvature bound |
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