Abels, Helmut and Grubb, G. and Wood, I. (2010) Extension Theory and Krein-type Resolvent Formulas for Nonsmooth Boundary Value Problems. arxiv.org . (Submitted)
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| Official URL http://arxiv.org/pdf/1008.3281v1.pdf |
Abstract
For a strongly elliptic second-order operator $A$ on a bounded domain $\Omega\subset \mathbb{R}^n$ it has been known for many years how to interpret the general closed $L_2(\Omega)$-realizations of $A$ as representing boundary conditions (generally nonlocal), when the domain and coefficients are smooth. The purpose of the present paper is to extend this representation to nonsmooth domains and coefficients, including the case of H\"older $C^{\frac32+\varepsilon}$-smoothness, in such a way that pseudodifferential methods are still available for resolvent constructions and ellipticity considerations. We show how it can be done for domains with $B^\frac32_{2,p}$-smoothness and operators with $H^1_q$-coefficients, for suitable $p>2(n-1)$ and $q>n$. In particular, Kre\u\i{}n-type resolvent formulas are established in such nonsmooth cases. Some unbounded domains are allowed.
| Item Type: | Article |
|---|---|
| Subjects: | Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations |
| Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science |
| Depositing User: | Ian Wood |
| Date Deposited: | 12 Oct 2012 15:33 |
| Last Modified: | 01 Mar 2013 11:17 |
| Resource URI: | http://kar.kent.ac.uk/id/eprint/31658 (The current URI for this page, for reference purposes) |
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