Eigenvalue asymptotics for potential type operators on Lipschitz surfaces

DOI10.1134/S1061920806030083zbMath1123.35037OpenAlexW1982684665MaRDI QIDQ871779

N. E. Zubov

Publication date: 26 March 2007

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1061920806030083

zbMATH Keywords

eigenvalue asymptoticspseudodifferential operatorpotential type operatorscompact Lipschitz surface

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Integral operators (47G10) Eigenvalue problems for integral equations (45C05)

Related Items (13)

Eigenvalues of singular measures and Connes' noncommutative integration ⋮ Eigenvalue asymptotics for potential type operators on Lipschitz surfaces of codimension greater than 1 ⋮ Weyl's law for the eigenvalues of the Neumann-Poincaré operators in three dimensions: Willmore energy and surface geometry ⋮ Strongly elliptic second-order systems with boundary conditions on a nonclosed Lipschitz surface ⋮ Mixed problems in a Lipschitz domain for strongly elliptic second-order systems ⋮ Spectral problems in Lipschitz domains ⋮ Spectral estimates and asymptotics for integral operators on singular sets ⋮ Weyl asymptotics for Poincaré-Steklov eigenvalues in a domain with Lipschitz boundary ⋮ Eigenvalue asymptotics for weighted polyharmonic operator with a singular measure in the critical case ⋮ Eigenvalues of the Neumann–Poincaré operator in dimension 3: Weyl’s law and geometry ⋮ Eigenvalue estimates and asymptotics for weighted pseudodifferential operators with singular measures in the critical case ⋮ Spectral problems in Sobolev-type Banach spaces for strongly elliptic systems in Lipschitz domains ⋮ Eigenvalues of the Birman-Schwinger operator for singular measures: the noncritical case

Cites Work

• Estimates of \(s\)-numbers and spectral asymptotics for integral operators of potential type on nonsmooth surfaces
• Singular Green operators and their spectral asymptotics
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• On the Hausdorff-Young theorem for integral operators
• Spectral problems for second-order strongly elliptic systems in smooth and non-smooth domains
• ASYMPTOTIC BEHAVIOR OF THE SPECTRUM OF WEAKLY POLAR INTEGRAL OPERATORS
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