Universität zu Köln

Kawohl, Bernd ORCID: 0000-0003-2918-7318, Kroemer, Stefan and Kurtz, Jannis (2014). RADIAL EIGENFUNCTIONS FOR THE GAME-THEORETIC p-LAPLACIAN ON A BALL. Differ. Integral Equ., 27 (7-8). S. 659 - 671. ATHENS: KHAYYAM PUBL CO INC. ISSN 0893-4983

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Abstract

The normalized or game-theoretic p-Laplacian operator given by APNU -Delta(N)(p)u := -1/p vertical bar VU vertical bar(2-P)Delta(P)(u) for p is an element of (1, infinity) with Delta(p)u = div (vertical bar Vu vertical bar(P-2)Delta u) has no apparent variational structure. Showing the existence of a first (positive) eigenvalue of this fully nonlinear operator requires heavy machinery as in [6]. If it is restricted to the class of radial functions, however, the normalized p-Laplacian transforms into a linear Sturm-Liouville operator. We investigate radial eigenfunctions to this operator under homogeneous Dirichlet boundary conditions and come up with an explicit complete orthonormal system of Bessel functions in a suitably weighted L-2-space. This allows us to give a Fourier-series representation for radial solutions to the corresponding evolution equation u(t) - Delta(N)(p)u = 0.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kawohl, Bernd UNSPECIFIED orcid.org/0000-0003-2918-7318 UNSPECIFIED Kroemer, Stefan UNSPECIFIED UNSPECIFIED UNSPECIFIED Kurtz, Jannis UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-435072
Journal or Publication Title:	Differ. Integral Equ.
Volume:	27
Number:	7-8
Page Range:	S. 659 - 671
Date:	2014
Publisher:	KHAYYAM PUBL CO INC
Place of Publication:	ATHENS
ISSN:	0893-4983
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 STURM-LIOUVILLE THEORY; NONLINEAR EIGENVALUES; ASYMPTOTIC-BEHAVIOR; OPERATORS; BIFURCATION; EQUATIONS Multiple languages Mathematics, Applied; Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/43507