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

Tynysbek Sharipovich Kalmenov, Michael Ruzhansky, Durvudkhan Suragan

Research output: Contribution to journalArticle

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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Spectral Geometry
Bessel Potential
Bessel Operator
Potential Operators
Nonlocal Boundary Value Problems
Helmholtz equation
Isoperimetric Inequality
Helmholtz Equation
Rayleigh
Mathematical operators
Differential operator
Euclidean
Valid
Analogue
Eigenvalue
Operator
Boundary value problems
Geometry

Keywords

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

ASJC Scopus subject areas

  • Modelling and Simulation

Cite this

On spectral and boundary properties of the volume potential for the Helmholtz equation. / Kalmenov, Tynysbek Sharipovich; Ruzhansky, Michael; Suragan, Durvudkhan.

In: Mathematical Modelling of Natural Phenomena, Vol. 14, No. 5, 502, 01.01.2019.

Research output: Contribution to journalArticle

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