On spectral and boundary properties of the volume potential for the Helmholtz equation

Tynysbek Sharipovich Kalmenov, Michael Ruzhansky, Durvudkhan Suragan

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Abstract

In this paper, we study boundary properties and some questions of spectral geometry for certain volume potential type operators (Bessel potential operators) in an open bounded Euclidean domains. In particular, the results can be valid for differential operators, which are related to a nonlocal boundary value problem for the Helmholtz equation, so we obtain isoperimetric inequalities for its eigenvalues as well, namely, analogues of the Rayleigh-Faber-Krahn inequality.

Original languageEnglish
Article number502
JournalMathematical Modelling of Natural Phenomena
Volume14
Issue number5
DOIs
Publication statusPublished - Jan 1 2019

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Keywords

  • Bessel potential
  • Boundary value problem
  • Helmholtz equation
  • Rayleigh-Faber-Krahn inequality
  • Schatten p-norm

ASJC Scopus subject areas

  • Modelling and Simulation

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