Point Source Equilibrium Problems with Connections to Weighted\n Quadrature Domains

2022/03/17 by Peter D Dragnev, Dragnev, Peter D., Alan R. Legg +3
Computer Science · Mathematics · #31A05 #31A10 #31A15 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2203.09421

openalex publication_date 2022/03/17 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We explore the connection between supports of equilibrium measures and\nquadrature identities, especially in the case of point sources added to the\nexternal field Q(z)=|z|^2p with p \∈ \ℕ. Along the way, we\ndescribe some quadrature domains with respect to weighted area measure\n|z|^2pdA_z and complex boundary measure |z|^-2pdz.\n

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