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arXiv · 2306.00232

Convergence of interfaces in boundary reactions

Aditya Kumar
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Abstract

In this paper we study the singular limit for critical points of boundary reactions \begin{equation*} (-Δ)^{\frac{1}{2}}u = \frac{1}{\varepsilon}(u-u^3) \quad \text{in } U \subset \textbf{R}^n . \end{equation*} We show the existence of a $(n-1)$-rectifiable energy concentration set. Furthermore, we show that the limit of the energy measures can be associated to a stationary, $(n-1)$-rectifiable varifold supported in the concentration set. This is analogous to a result of Hutchinson and Tonegawa for phase transitions.

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Aditya Kumar. 2023-05-31. Convergence of interfaces in boundary reactions. https://arxiv.org/abs/2306.00232

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