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arXiv · 2403.09382

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

Nikolay Kuznetsov
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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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Nikolay Kuznetsov. 2024-03-14. The convexity of a planar domain via properties of solutions to the modified Helmholtz equation. https://arxiv.org/abs/2403.09382

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