# Elliptic differential operators on Lipschitz domains and abstract boundary value problems

@article{Behrndt2014EllipticDO,
title={Elliptic differential operators on Lipschitz domains and abstract boundary value problems},
author={Jussi Behrndt and Till Micheler},
journal={Journal of Functional Analysis},
year={2014},
volume={267},
pages={3657 - 3709}
}
• Published 29 July 2013
• Mathematics
• Journal of Functional Analysis
35 Citations
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## References

SHOWING 1-10 OF 89 REFERENCES
On Non-local Boundary Value Problems for Elliptic Operators
In this thesis we study non-local boundary value problems for elliptic differential operators on manifolds with smooth boundary. First of all a theory for general elliptic operators is developed.
A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains
• Mathematics
• 2009
This paper has two main goals. First, we are concerned with a description of all self-adjoint extensions of the Laplacian $$- \Delta {|_{C_0^\infty (\Omega )}}$$ in L2(Ω; dnx). Here, the domain Ω
Perturbation of essential spectra of exterior elliptic problems
For a second-order symmetric strongly elliptic differential operator on an exterior domain in ℝ n , it is known from the works of Birman and Solomiak that a change in the boundary condition from the
Trace formulae and singular values of resolvent power differences of self‐adjoint elliptic operators
• Mathematics
J. Lond. Math. Soc.
• 2013
In this note, self‐adjoint realizations of second‐order elliptic differential expressions with non‐local Robin boundary conditions on a domain Ω ⊂ ℝn with smooth compact boundary are studied. A
Boundary relations and generalized resolvents of symmetric operators
• Mathematics
• 2006
The Kreĭn-Naĭmark formula provides a parametrization of all selfadjoint exit space extensions of a (not necessarily densely defined) symmetric operator in terms of maximal dissipative (in ℂ+)
A general boundary value problem and its Weyl function
We study the abstract boundary value problem defined in terms of the Green identity and introduce the concept of Weyl operator function $$M(\cdot)$$ that agrees with other definitions found in the