Abels, Helmut and Grubb, Gerd and Wood, Ian Geoffrey (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, 1096-0783
Full text not available from this repository. (Request a copy)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 Krein resolvent formulas, of the realizations of nonselfadjoint second-order operators on C3/2+epsilon domains; more precisely, we treat domains with B-p,2(3/2)-smoothness and operators with H-q(1)-coefficients, for suitable p > 2(n - 1) and q > n. 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. (C) 2014 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PSEUDODIFFERENTIAL-OPERATORS; COEFFICIENTS; EQUATIONS; BESOV; Extension theory; Krein resolvent formula; Elliptic boundary value problems; Pseudodifferential boundary operators; Symbol smoothing; M-functions; Nonsmooth domains; Nonsmooth coefficients |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Nov 2019 11:44 |
| Last Modified: | 15 Nov 2019 11:44 |
| URI: | https://pred.uni-regensburg.de/id/eprint/10419 |
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