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Extension Theory and Krein-type Resolvent Formulas for Nonsmooth Boundary Value Problems

Abels, Helmut, Grubb, Gerd, Wood, Ian (2014) Extension Theory and Krein-type Resolvent Formulas for Nonsmooth Boundary Value Problems. Journal of Functional Analysis, 266 (7). pp. 4037-4100. ISSN 0022-1236. (doi:10.1016/j.jfa.2014.01.016) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:31658)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
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Abstract

The theory of selfadjoint extensions of symmetric operators, and more generally the theory of extensions of dual pairs, was implemented some years ago for boundary value problems for elliptic operators on smooth bounded domains. Recently, the questions have been taken up again for nonsmooth domains. In the present work we show that pseudodifferential methods can be used to obtain a full characterization, including Kreĭn resolvent formulas, of the realizations of nonselfadjoint second-order operators on domains; more precisely, we treat domains with -smoothness and operators with -coefficients, for suitable and . The advantage of the pseudodifferential boundary operator calculus is that the operators are represented by a principal part and a lower-order remainder, leading to regularity results; in particular we analyze resolvents, Poisson solution operators and Dirichlet-to-Neumann operators in this way, also in Sobolev spaces of negative order.

Item Type: Article
DOI/Identification number: 10.1016/j.jfa.2014.01.016
Uncontrolled keywords: Extension theory; Krein resolvent formula; Elliptic boundary value problems; Pseudodifferential boundary operators; Symbol smoothing; M-functions; Nonsmooth domains; Nonsmooth coefficients
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Ian Wood
Date Deposited: 12 Oct 2012 15:33 UTC
Last Modified: 22 Jan 2020 11:41 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/31658 (The current URI for this page, for reference purposes)
Wood, Ian: https://orcid.org/0000-0001-7181-7075
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