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arXiv · 1903.03185

On the concentration for a singularly perturbed problem with nonlinear Neumann boundary condition

Eduardo Hitomi
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Abstract

In this work, we prove the existence of a family of solutions of the Allen-Cahn equation with nonlinear Neumann boundary condition under some constraints, whose nodal sets concentrate asymptotically to a given volume nondegenerate capillary hypersurface in a compact Riemannian manifold. Our construction is inspired by the works of Pacard and of Pacard and Ritor\'e.

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Eduardo Hitomi. 2019-03-07. On the concentration for a singularly perturbed problem with nonlinear Neumann boundary condition. https://arxiv.org/abs/1903.03185

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