Nagoya Mathematical Journal

Existence of functions in weighted Sobolev spaces

Toshihide Futamura and Yoshihiro Mizuta

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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.

Article information

Nagoya Math. J., Volume 164 (2001), 75-88.

First available in Project Euclid: 27 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Secondary: 31B15: Potentials and capacities, extremal length 31C45: Other generalizations (nonlinear potential theory, etc.)


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

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