Hölder estimates of p-harmonic extension operators |
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Authors: | Hiroaki Aikawa Nageswari Shanmugalingam |
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Institution: | a Department of Mathematics, Shimane University, Nishi Kawatsu 1060, Matsue 690-8504, Japan b Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, Cincinnati, OH 45221-0025, USA |
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Abstract: | It is now a well-known fact that for 1<p<∞ the p-harmonic functions on domains in metric measure spaces equipped with a doubling measure supporting a (1,p)-Poincaré inequality are locally Hölder continuous. In this note we provide a characterization of domains in such metric spaces for which p-harmonic extensions of Hölder continuous boundary data are globally Hölder continuous. We also provide a link between this regularity property of the domain and the uniform p-fatness of the complement of the domain. |
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Keywords: | 35J65 35J25 31C45 31B25 31B05 |
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