Boundary spike of the singular limit of an energy minimizing problem

Xinfu Chen; Huiqiang Jiang; Guoqing Liu

doi:10.3934/dcds.2020124

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2020, Volume 40, Issue 6: 3253-3290. Doi: 10.3934/dcds.2020124 open access

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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: March 2020

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

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Abstract

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.

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

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