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

DOI10.1051/mmnp/2019001zbMath1419.35141OpenAlexW2932565659MaRDI QIDQ5229666

Michael Ruzhansky, Durvudkhan Suragan, Tynysbek Sh. Kal'menov

Publication date: 16 August 2019

Published in: Mathematical Modelling of Natural Phenomena (Search for Journal in Brave)

Full work available at URL: https://www.mmnp-journal.org/10.1051/mmnp/2019001/pdf

zbMATH Keywords

boundary value problemHelmholtz equationBessel potentialSchatten \(p\)-normRayleigh-Faber-Krahn inequality

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Boundary value problems for PDEs with pseudodifferential operators (35S15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Potential operators (47G40)

Cites Work

• Isoperimetric inequalities for Schatten norms of Riesz potentials
• On first and second eigenvalues of Riesz transforms in spherical and hyperbolic geometries
• Analytic formulas for the topological degree of non-smooth mappings: The odd-dimensional case
• Boundary conditions for the volume potential for the polyharmonic equation
• Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups
• Theory of Bessel potentials. I
• On transparent boundary conditions for the high-order heat equation
• Isoperimetric inequalities for the logarithmic potential operator
• To spectral problems for the volume potential
• Weak type estimates for singular values and the number of bound states of Schrödinger operators
• A general rearrangement inequality for multiple integrals
• Leading term in the asymptotic spectral formula for nonsmooth elliptic problems
• On Schatten norms of convolution-type integral operators
• Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator
• ASYMPTOTIC BEHAVIOR OF THE SPECTRUM OF WEAKLY POLAR INTEGRAL OPERATORS
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On spectral and boundary properties of the volume potential for the Helmholtz equation