Density Results in Sobolev Spaces Whose Elements Vanish on a Part of the Boundary

作     者：Jean-Marie Emmanuel BERNARD 

作者机构：Laboratoire Analyse et ProbabitilitésUniversité d'Evry val d'Essonne23 Boulevard de France91037 EVRYFrance 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2011年第32卷第6期

页      面：823-846页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Density results Boundary value problems Sobolev spaces 

摘      要：This paper is devoted to the study of the subspace of Wm＇＂ of functions that vanish on a part γ0 of the boundary. The author gives a crucial estimate of the Poincare constant in balls centered on the boundary of γ0. Then, the convolution-translation method, a variant of the standard mollifier technique, can be used to prove the density of smooth functions that vanish in a neighborhood of γ0, in this subspace. The result is first proved for m = 1, then generalized to the case where m 〉 1, in any dimension, in the framework of Lipschitz-continuous domain. However, as may be expected, it is needed to make additional assumptions on the boundary of γ0, namely that it is locally the graph of some Lipschitz-continuous function.