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Boundary spike of the singular limit of an energy minimizing problem

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

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  • 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.

    Mathematics Subject Classification: Primary: 35J20, 74K35; Secondary: 34B18.


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