A boundary uniqueness theorem for Sobolev functions
type: Item
instance of: scholarly article
title: A boundary uniqueness theorem for Sobolev functions
zbMATH Open document ID: 0914.31003
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1999-06-20T00:00:00Z
review text: Uniqueness theorems for analytic functions having zero radial limits on a set of positive capacity are well known. The authors obtain a result of such a kind for continuous functions \(u\) in \(\mathbb{R}^n\) with a finite seminorm \(\int_{\mathcal{B}}| \nabla u| ^p dm\), \(\mathcal{B}\) being a bounded domain in \(\mathbb{R}^n\). This result is formulated in terms of the behaviour of the functional \[ I(\varepsilon)=\int_{x\in\mathcal{B}, | u(x)| < \varepsilon}| \nabla u| ^p dm \] as \(\varepsilon \to 0\).
Mathematics Subject Classification ID: 31B25
zbMATH DE Number: 1275222
zbMATH Keywords: analytic functions
zbMATH Keywords: boundary value
zbMATH Keywords: zero sets
zbMATH Keywords: Dirichlet integral
author: V. M. Miklyukov
author: M. Vuorinen
reviewed by: S. G. Samko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178224894
OpenAlex ID: W2128163086
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DOI: 10.2748/TMJ/1178224894
description: scientific article; zbMATH DE number 1275222