Sturm-Liouville problems in domains with non-smooth edges

We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain for a second order elliptic differential operator A. The differential operator is assumed to be of divergent form and the boundary operator B is of Robin type. The boundary is assumed to be a Lipschitz surface. Besides, we distinguish a closed subset of the boundary and control the growth of solutions near this set. We prove that the pair (A,B) induces a Fredholm operator L in suitable weighted spaces of Sobolev type, the weight function being a power of the distance to the singular set. Moreover, we prove the completeness of root functions related to L.

Metadaten
Author details:	Alexander Shlapunov ORCiD GND, Nikolai Nikolaevich Tarkhanov ORCiD GND
URN:	urn:nbn:de:kobv:517-opus-67336
Publication series (Volume number):	Preprints des Instituts für Mathematik der Universität Potsdam (2(2013)13)
Publication type:	Preprint
Language:	English
Publication year:	2013
Publishing institution:	Universität Potsdam
Release date:	2013/08/28
Tag:	Second order elliptic equations; non-coercive boundary conditions; root functions; weighted spaces
Organizational units:	Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:	5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC classification:	35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B25 Singular perturbations
	35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J60 Nonlinear elliptic equations
Collection(s):	Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2013
License (German):	Keine öffentliche Lizenz: Unter Urheberrechtsschutz