Krein resolvent formulas for elliptic boundary problems in nonsmooth domains
arXiv:0810.2741
Abstract
The paper reports on a recent construction of M-functions and Krein resolvent formulas for general closed extensions of an adjoint pair, and their implementation to boundary value problems for second-order strongly elliptic operators on smooth domains. The results are then extended to domains with Hölder smoothness, by use of a recently developed calculus of pseudodifferential boundary operators with nonsmooth symbols.
28 pages. For the Rendiconti Torino volume in honor of Luigi Rodino
References in corpus (3)
Cited by in corpus (13)
- Spectral Theory for Perturbed Krein Laplacians in Nonsmooth Domains
- A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains
- Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces
- Spectral estimates for resolvent differences of self-adjoint elliptic operators
- Symmetrized Perturbation Determinants and Applications to Boundary Data Maps and Krein-Type Resolvent Formulas
- Spectral enclosures for non-self-adjoint extensions of symmetric operators
- Quasi boundary triples and semibounded self-adjoint extensions
- Markovian Extensions of Symmetric Second Order Elliptic Differential Operators
- An abstract inverse problem for boundary triples with an application to the Friedrichs Model
- First-order asymptotic perturbation theory for extensions of symmetric operators
- A class of nonlinear elliptic boundary value problems
- A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains
- Boundary Data Maps for Schrodinger Operators on a Compact Interval