On the regularity of critical and minimal sets of a free interface problem

2013/09/26 by Nicola Fusco, Fusco, Nicola, Vesa Julin +1 · 2 citations
Computer Science · Engineering · Mathematics · #49N60 #49Q10 #74G40 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP #msc:49N60 #msc:49Q10 #msc:74G40

paper · pdf · doi:10.48550/arxiv.1309.6810

openalex publication_date 2013/09/26 · arxiv created 2014/05/26 · arxiv updated 2014/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a free interface problem of finding the optimal energy configuration for mixtures of two conducting materials with an additional perimeter penalization of the interface. We employ the regularity theory of linear elliptic equations to study the possible opening angles of Taylor cones and to give a different proof of a partial regularity result by Fan Hua Lin.

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