The convexity of a planar domain via properties of solutions to the modified Helmholtz equation

2024/03/14 by Н. В. Кузнецов, Kuznetsov, Nikolay
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2403.09382

openalex publication_date 2024/03/14 · openalex created_date 2024/03/16 · openalex updated_date 2026/07/28

Abstract

A new characterization of convexity of a planar domain is obtained. Its derivation involves two classical facts: the Varadhan's formula, expressing the distance function with respect to the domain's boundary via real-valued solutions of the modified Helmholtz equation, and the convexity of a planar domain in which the distance function is superharmonic

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