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

Abels, Helmut and Grubb, Gerd and 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. (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)

 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) Official URLhttp://www.sciencedirect.com/science/article/pii/S...

## 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 Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, CalculusQ Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science Ian Wood 12 Oct 2012 15:33 28 Jul 2014 08:11 https://kar.kent.ac.uk/id/eprint/31658 (The current URI for this page, for reference purposes)