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The Convexity of a Planar Domain Via Properties of Solutions to the Modified Helmholtz Equation

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

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Authors and Affiliations

  1. Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, RAS, V.O., Bol’shoy pr. 61, St Petersburg, 199178, Russia

    N. Kuznetsov

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  1. N. Kuznetsov
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Correspondence to N. Kuznetsov.

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To N. N. Uraltseva with admiration

Translated from Problemy Matematicheskogo Analiza 127, 2024, pp. 117-120.

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Kuznetsov, N. The Convexity of a Planar Domain Via Properties of Solutions to the Modified Helmholtz Equation. J Math Sci 281, 607–611 (2024). https://doi.org/10.1007/s10958-024-07137-6

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  • DOI: https://doi.org/10.1007/s10958-024-07137-6

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