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2001 Existence of functions in weighted Sobolev spaces
Toshihide Futamura, Yoshihiro Mizuta
Nagoya Math. J. 164: 75-88 (2001).

Abstract

The aim of this paper is to determine when there exists a quasicontinuous Sobolev function $u \in W^{1,p}({\bf R}^n;\mu)$ whose trace $u|_{{\mathbf R}^{n-1}}$ is the characteristic function of a bounded set $E \subset {\bf R}^{n-1}$, where $d\mu(x) = |x_n|^\alpha dx$ with $-1< \alpha < p-1$. As application we discuss the existence of harmonic measures for weighted $p$-Laplacians in the unit ball.

Citation

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Toshihide Futamura. Yoshihiro Mizuta. "Existence of functions in weighted Sobolev spaces." Nagoya Math. J. 164 75 - 88, 2001.

Information

Published: 2001
First available in Project Euclid: 27 April 2005

zbMATH: 1023.46037
MathSciNet: MR1869095

Subjects:
Primary: 46E35
Secondary: 31B15, 31C45

Rights: Copyright © 2001 Editorial Board, Nagoya Mathematical Journal

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