ZERO SET OF SOBOLEV FUNCTIONS WITH NEGATIVE POWER OF INTEGRABILITY

作     者：JIANGHUIQIANG LINFANGHUA 

作者机构：CourantInstitute251MercerStreetNewYorkNY10009USA. 

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

年 卷 期：2004年第25卷第1期

页      面：65-72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：Singular elliptic equation Poincare inequality Thin film Partial regu- larity Zero set Rupture set Hausdorff dimension 

摘      要：Here the authors are interested in the zero set of Sobolev functions and functions of bounded variation with negative power of integrability. The main result is a general Hausdorff dimension estimate on the size of zero set. The research is motivated by the model on van der waal force driven thin film, which is a singular elliptic equation. After obtaining some basic regularity result, the authors get an estimate on the size of singular set; such set corresponds to the thin film rupture set in the thin film model.