### 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) |
---|---|

Pages (from-to) | 65-72 |

Number of pages | 8 |

Journal | Chinese Annals of Mathematics. Series B |

Volume | 25 |

Issue number | 1 |

DOIs | |

State | Published - 2004 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Chinese Annals of Mathematics. Series B*, vol. 25, no. 1, pp. 65-72. https://doi.org/10.1142/S0252959904000068

}

TY - JOUR

T1 - Zero set of Sobolev functions with negative power of integrability

AU - Jiang, Huiqiang

AU - Lin, Fang-Hua

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

KW - Hausdorff dimension

KW - Partial regularity

KW - Poincare inequality

KW - Rupture set

KW - Singular elliptic equation

KW - Thin film

KW - Zero set

UR - http://www.scopus.com/inward/record.url?scp=4444381824&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4444381824&partnerID=8YFLogxK

U2 - 10.1142/S0252959904000068

DO - 10.1142/S0252959904000068

M3 - Article

AN - SCOPUS:4444381824

VL - 25

SP - 65

EP - 72

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

SN - 0252-9599

IS - 1

ER -