### 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 language | English (US) |
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Pages (from-to) | 65-72 |

Number of pages | 8 |

Journal | Chinese Annals of Mathematics. Series B |

Volume | 25 |

Issue number | 1 |

DOIs | |

State | Published - Sep 22 2004 |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics