| ZERO SET OF SOBOLEV FUNCTIONS WITH NEGATIVE POWER OF INTEGRABILITY |
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| 作者姓名： | JIANG Huiqiang LIN Fanghua |
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| 作者单位： | JIANG Huiqiang LIN Fanghua Courant Institute，251 Mercer Street，New York，NY，10009，USA.Courant Institute，251 Mercer Street，New York，NY，10009，USA. |
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| 摘 要： | §1. Introduction Let ? ? Rn (n ≥1) be an open set, p ≥1. We consider functions u ∈W1 (?), such ,pthat, for some α> 0, |u|? < ∞. α (1.1) ?When p = 1, it is also natural to consider u ∈BV (?) which satis?es (1.1). For any u ∈W1 (?), p ≥1 or u ∈BV (?), we de?ne its zero set by …
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| 关 键 词： | 零集 SOBOLEV函数 可积分性 椭圆方程 |
| 收稿时间： | 2/3/2011 12:00:00 AM |
| 修稿时间： | 5/3/2026 12:00:00 AM |
ZERO SET OF SOBOLEV FUNCTIONS WITH NEGATIVE POWER OF INTEGRABILITY |
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| JIANG Huiqiang,LIN Fanghua.ZERO SET OF SOBOLEV FUNCTIONS WITH NEGATIVE POWER OF INTEGRABILITY[J].Chinese Annals of Mathematics,Series B,2004,25(1):65-72. |
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| Authors: | JIANG Huiqiang and LIN Fanghua |
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| Institution: | Courant Institute, 251 Mercer Street, New York, NY, 10009, USA |
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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. |
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| Keywords: | Singular elliptic equation Poincare inequality Thin film Partial regu- larity Zero set Rupture set Hausdorff dimension |
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