Logarithmic Convexity for Supremum Norms of Harmonic Functions |
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Authors: | Korevaar, J. Meyers, J. L. H. |
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Affiliation: | Faculty of Mathematics and Computer Science, University of Amsterdam Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands |
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Abstract: | We prove the following convexity property for supremum normsof harmonic functions. Let be a domain in Rn, 0 and E a subdomainand a compact sebset of ,respectively. Then there exists a constant = (E, 0, ) (0, 1) such that for all harmonic functions u on, the inequality is valid.The case of concentric balls E plays a key role in the proof.For positive harmonic funcitons ono osuch balls, we determinethe sharp constant in the inequlity. |
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