Extension theory and Kreĭn-type resolvent formulas for nonsmooth boundary value problems
@article{Abels2010ExtensionTA, title={Extension theory and Kreĭn-type resolvent formulas for nonsmooth boundary value problems}, author={Helmut Abels and Gerd Grubb and Ian Wood}, journal={Journal of Functional Analysis}, year={2010}, volume={266}, pages={4037-4100} }
38 Citations
EXTENSION THEORY FOR ELLIPTIC PARTIAL DIFFERENTIAL OPERATORS WITH PSEUDODIFFERENTIAL METHODS
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- 2010
This is a short survey on the connection between general extension theories and the study of realizations of elliptic operators A on smooth domains in R n , n � 2. The theory of pseudodifferential…
The mixed boundary value problem, Krein resolvent formulas and spectral asymptotic estimates
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- 2011
Regularity of spectral fractional Dirichlet and Neumann problems
- Mathematics
- 2016
Consider the fractional powers (ADir)a and (ANeu)a of the Dirichlet and Neumann realizations of a second‐order strongly elliptic differential operator A on a smooth bounded subset Ω of Rn . Recalling…
Spectral Asymptotics for Nonsmooth Singular Green Operators
- Mathematics
- 2012
Singular Green operators G appear typically as boundary correction terms in resolvents for elliptic boundary value problems on a domain Ω ⊂ ℝ n , and more generally they appear in the calculus of…
Nonsmooth pseudodifferential boundary value problems on manifolds
- MathematicsJournal of Pseudo-Differential Operators and Applications
- 2018
We study pseudodifferential boundary value problems in the context of the Boutet de Monvel calculus or Green operators, with nonsmooth coefficients on smooth compact manifolds with boundary. In order…
Elliptic differential operators on Lipschitz domains and abstract boundary value problems
- MathematicsJournal of functional analysis
- 2014
Inverse problems with partial data for elliptic operators on unbounded Lipschitz domains
- MathematicsInverse Problems
- 2020
For a second order formally symmetric elliptic differential expression we show that the knowledge of the Dirichlet-to-Neumann map or Robin-to-Dirichlet map for suitably many energies on an…
Krein-like extensions and the lower boundedness problem for elliptic operators on exterior domains
- Mathematics
- 2010
δ′-Potentials Supported on Hypersurfaces
- Mathematics
- 2012
Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are…
SPECTRAL ASYMPTOTICS FOR ROBIN PROBLEMS WITH A DISCONTINUOUS COEFFICIENT
- Mathematics
- 2011
The spectral behavior of the difference between the resolvents of two realizations z A1 and z A2 of a second-order strongly elliptic symmetric differential operator A ,d ef ined by different Robin…
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Singular Green operators G appear typically as boundary correction terms in resolvents for elliptic boundary value problems on a domain Ω ⊂ ℝ n , and more generally they appear in the calculus of…
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THEORY 1. The general set-up. The study of extensions of linear operators in Hilbert space is a well known tool in the theory of boundary value problems. The basic notions for the framework used here…