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arXiv · 1502.04212

Singular perturbation by bending for an adhesive obstacle problem

Tatsuya Miura
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Abstract

A free boundary problem arising from materials science is studied in one-dimensional case. The problem studied here is an obstacle problem for the non-convex energy consisting of a bending energy, tension and an adhesion energy. If the bending energy, which is a higher order term, is deleted then "edge" singularities of the solutions (surfaces) may occur at the free boundary as Alt-Caffarelli type variational problems. The main result of this paper is to give a singular limit of the energy utilizing the notion of $\Gamma$-convergence, when the bending energy can be regarded as a perturbation. This singular limit energy only depends on the state of surfaces at the free boundary as seen in singular perturbations for phase transition models.

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Tatsuya Miura. 2015-02-14. Singular perturbation by bending for an adhesive obstacle problem. https://doi.org/10.1007/s00526-015-0941-z

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