Traces of monotone Sobolev functions |
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Authors: | Juan J Manfredi Enrique Villamor |
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Institution: | 1. Department of Mathematics, University of Pittsburgh, 15260, Pittsburgh, PA 2. Department of Mathematics, Florida International University, 33199, Miami, FL
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Abstract: | In this paper we prove that ifu: ${\mathbb{B}}^n \to {\mathbb{R}}$ , where ${\mathbb{B}}^n $ is the unit ball in ? n , is a monotone function in the Sobolev space W1·p ( ${\mathbb{B}}^n $ ), andn ? 1 <p ≤n, thenu has nontangential limits at all the points of $\partial {\mathbb{B}}^n $ except possibly on a set ofp-capacity zero. The key ingredient in the proof is an extension of a classical theorem of Lindelöf to monotone functions in W1·p ( ${\mathbb{B}}^n $ ),n ? 1 <p ≤n. |
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