Convergence of interfaces in boundary reactions

2023/05/31 by Kumar, Aditya
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2306.00232

openalex publication_date 2023/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the singular limit for critical points of boundary reactions (-Δ)^(1)/(2)u = (1)/(ε)(u-u³) in U ⊂ Rⁿ . 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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