Zero set of Sobolev functions with negative power of integrability

Huiqiang Jiang, Fanghua Lin

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)65-72
Number of pages8
JournalChinese Annals of Mathematics. Series B
Volume25
Issue number1
DOIs
StatePublished - 2004

Keywords

  • Hausdorff dimension
  • Partial regularity
  • Poincare inequality
  • Rupture set
  • Singular elliptic equation
  • Thin film
  • Zero set

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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