2015/11/09 by Avetik Arakelyan, Henrik Shahgholian, Arakelyan, Avetik +1
Computer Science · Engineering · Mathematics · #35B06 #35R35 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1511.02779
openalex publication_date 2015/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce the multi-phase version of the so-called Quadrature Domains (QD), which refers to a generalized type of mean value property for harmonic functions. The well-established and developed theory of one-phase QD was recently generalized to a two-phase version, by one of the current authors (in collaboration). Here we introduce the concept of the multi-phase version of the problem, and prove existence as well as several properties of such solutions. In particular, we discuss possibilities of multi-junction points.