# American Institute of Mathematical Sciences

March  2011, 10(2): 803-815. doi: 10.3934/cpaa.2011.10.803

## Energy minimizers of a thin film equation with born repulsion force

 1 Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, United States

Received  January 2010 Revised  May 2010 Published  December 2010

In this paper, we consider a singular elliptic equation modeling steady states of thin film equation with both Van der Waal force and Born repulsion force. We prove the existence of smooth positive energy minimizing solutions. We also investigate the regularity of local minimizers and the limiting behavior of energy minimizer as the Born repulsion force tends to zero.
Citation: Huiqiang Jiang. Energy minimizers of a thin film equation with born repulsion force. Communications on Pure & Applied Analysis, 2011, 10 (2) : 803-815. doi: 10.3934/cpaa.2011.10.803
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