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Extension theory and Kreĭn-type resolvent formulas for nonsmooth boundary value problems

Abels, Helmut and Grubb, Gerd and Wood, Ian G. (2010) Extension theory and Kreĭn-type resolvent formulas for nonsmooth boundary value problems. Preprintreihe der Fakultät Mathematik 13/2010, Working Paper. (Unpublished)

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Abstract

For a strongly elliptic second-order operator A on a bounded domain Rn it has been known for many years how to interpret the general closed L2()-realizations of A
as representing boundary conditions (generally nonlocal), when the domain and coeffcients are smooth. The purpose of the present paper is to extend this representation to
nonsmooth domains and coeffcients, including the case of Hölder C 3/2+"-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 3/2 2;p-smoothness and operators with H1 q -coeffcients, for suitable p > 2(n

Item Type:

Monograph (Working Paper)

Institutions:

Mathematics > Prof. Dr. Helmut Abels

Classification:

Notation	Type
35J25	MSC
35P05	MSC
35S15	MSC
47A10	MSC
47A20	MSC
47G30	MSC

Keywords:

Elliptic boundary value problems; pseudodifferential boundary operators; extension theory; M-functions; symbol smoothing; nonsmooth domains; nonsmooth coeffcients

Subjects:

500 Science > 510 Mathematics

Status:

Unpublished

Refereed:

No, this version has not been refereed yet (as with preprints)

Created at the University of Regensburg:

Yes

Owner:

Universitätsbibliothek Regensburg

Deposited On:

13 Apr 2011 05:41