Universität zu Köln

Schnieders, Inka ORCID: 0000-0002-4895-0000 and Sweers, Guido ORCID: 0000-0003-0180-5890 (2020). A biharmonic converse to Krein-Rutman: a maximum principle near a positive eigenfunction. Positivity, 24 (3). S. 677 - 711. DORDRECHT: SPRINGER. ISSN 1572-9281

Full text not available from this repository.

Abstract

The Green function G(0)(x,y) for the biharmonic Dirichlet problem on a smooth domain Omega, that is Delta(2)u=f in Omega with u=u(n)=0 on partial derivative Omega, can be written as the difference of a positive function, which bears the singularity at x=y, and a rank-one positive function, both of which satisfy the boundary conditions. See Grunau et al. (Proc Am Math Soc 139:2151-2161, 2011). More precisely G(0)(x,y)=H(x,y)-cd(x)(2)d(y)(2) holds, where d(.) is the distance to the boundary partial derivative Omega and where H contains the singularity and is positive. We will extend the corresponding estimates to G lambda(x,y) for the differential operator Delta(2)-lambda with an optimal dependence on lambda. As a consequence, strict positivity of an eigenfunction with a simple eigenvalue lambda(i) implies a positivity preserving property for (Delta(2)-lambda)u=f in Omega with u=u(n)=0 on partial derivative Omega for lambda in a left neighbourhood of lambda i. This result can be viewed as a converse to the Krein-Rutman theorem.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Schnieders, Inka UNSPECIFIED orcid.org/0000-0002-4895-0000 UNSPECIFIED Sweers, Guido UNSPECIFIED orcid.org/0000-0003-0180-5890 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-328542
DOI:	10.1007/s11117-019-00702-3
Journal or Publication Title:	Positivity
Volume:	24
Number:	3
Page Range:	S. 677 - 711
Date:	2020
Publisher:	SPRINGER
Place of Publication:	DORDRECHT
ISSN:	1572-9281
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language DIFFERENTIAL-EQUATIONS; POLYHARMONIC OPERATORS; GREEN-FUNCTION; EIGENVALUES; VALUES Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/32854