Krein's Resolvent Formula for Self-Adjoint Extensions of Symmetric Second Order Elliptic Differential Operators

Abstract

Given a symmetric, semi-bounded, second order elliptic differential operator on a bounded domain with $C^{1,1}$ boundary, we provide a Krein-type formula for the resolvent difference between its Friedrichs extension and an arbitrary self-adjoint one.

arXiv commentFinal version, to appear in J. Phys. A: Math. Theor

References in corpus (6)

• Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices
• Boundary triples and Weyl functions for singular perturbations of self-adjoint operators
• Self-Adjoint Extensions by Additive Perturbations
• First order operators and boundary triples
• M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems
• Self-adjoint Extensions of Restrictions

Cited by in corpus (14)

• Schrödinger operators with delta and delta'-potentials supported on hypersurfaces
• 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
• Krein resolvent formulas for elliptic boundary problems in nonsmooth domains
• An isoperimetric-type inequality for electrostatic shell interactions for Dirac operators
• Spectral estimates for resolvent differences of self-adjoint elliptic operators
• Symmetrized Perturbation Determinants and Applications to Boundary Data Maps and Krein-Type Resolvent Formulas
• Markovian Extensions of Symmetric Second Order Elliptic Differential Operators
• Inverse problems with partial data for elliptic operators on unbounded Lipschitz domains
• Linear Operators and Operator Functions Associated with Spectral Boundary Value Problems
• First-order asymptotic perturbation theory for extensions of symmetric operators
• The abstract Titchmarsh-Weyl M-function for adjoint operator pairs and its relation to the spectrum
• A class of nonlinear elliptic boundary value problems
• Generalized Q-functions and Dirichlet-to-Neumann maps for elliptic differential operators