# American Institute of Mathematical Sciences

June  2020, 40(6): 3253-3290. doi: 10.3934/dcds.2020124

## Boundary spike of the singular limit of an energy minimizing problem

 Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, USA

Received  February 2019 Revised  September 2019 Published  February 2020

Fund Project: This research is partially supported by the National Science Foundation grants DMS-0504691 and DMS-1200599

In this paper, we consider the singular limit of an energy minimizing problem which is a semi-limit of a singular elliptic equation modeling steady states of thin film equation with both Van der Waals force and Born repulsion force. We show that the singular limit of energy minimizers is a Dirac mass located on the boundary point with the maximum curvature.

Citation: Xinfu Chen, Huiqiang Jiang, Guoqing Liu. Boundary spike of the singular limit of an energy minimizing problem. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3253-3290. doi: 10.3934/dcds.2020124
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