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| ZERO SET OF SOBOLEV FUNCTIONS WITH NEGATIVE POWER OF INTEGRABILITY |
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Citation： |
JIANG Huiqiang,LIN Fanghua.ZERO SET OF SOBOLEV FUNCTIONS WITH NEGATIVE POWER OF INTEGRABILITY[J].Chinese Annals of Mathematics B,2004,25(1):65~72 |
| Page view： 1308
Net amount： 722 |
Authors： |
JIANG Huiqiang; LIN Fanghua |
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| 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. |
Keywords： |
Singular elliptic equation, Poincare inequality, Thin film, Partial regularity,
Zero set, Rupture set, Hausdorff dimension |
Classification： |
35J15, 49Q15, 74K35 |
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