A Radial Uniqueness Theorem for Sobolev Functions |
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Authors: | Koskela P |
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Institution: | Department of Mathematics, University of Michigan Ann Arbor, MI 48109, USA |
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Abstract: | We show that continuous functions u in the Sobolev space , 1 < p n, which have the limitzero in a certain weak sense in a set of positive p-capacityon B with
where B is the open unit ball of Rn and
for 0 > > , are identically zero. Conversely, we produce for each 1 > p n and each positive a non-constant function u in , continuous in , and a compact set EB of positive p-capacity such that u = 0 in E and the aboveinequality holds with exponent p l + . |
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Keywords: | |
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