Zero set of Sobolev functions with negative power of integrability

Huiqiang Jiang, Fang-Hua 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

Fingerprint

Zero set
Integrability
Thin Films
Thin films
Singular Elliptic Equation
Van Der Waals Force
Van der Waals forces
Functions of Bounded Variation
Singular Set
Rupture
Hausdorff Dimension
Estimate
Regularity
Model

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Zero set of Sobolev functions with negative power of integrability. / Jiang, Huiqiang; Lin, Fang-Hua.

In: Chinese Annals of Mathematics. Series B, Vol. 25, No. 1, 2004, p. 65-72.

Research output: Contribution to journalArticle

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