Universität zu Köln

Kruegel, Florian (2015). Potential theory for the sum of the 1-Laplacian and p-Laplacian. Nonlinear Anal.-Theory Methods Appl., 112. S. 165 - 181. OXFORD: PERGAMON-ELSEVIER SCIENCE LTD. ISSN 1873-5215

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Abstract

The variational problem of minimizing the functional u bar right arrow integral(Omega) vertical bar Du vertical bar + 1/p integral(Omega) vertical bar Du vertical bar(p) - integral(Omega) au on a domain Omega subset of R-n under zero boundary values, which appears for example in the theory of Bingham fluids, shows interesting phenomena such as the formation of a subset of Omega with positive measure where the minimizer is constant (a plateau''). The corresponding Euler-Lagrange equation should be -Lambda(1)u -Lambda(p)u = a, but the 1-Laplacian is not defined in points where Du = 0. We show that it is nevertheless possible to define subsolutions and supersolutions for this equation. We show that the comparison principle is valid, and we begin developing a potential theory analogous to what is known about the p-Laplacian. In addition we apply those notions to rotationally invariant solutions, and we discuss properties of the plateau and a possible connection to the theory. (C) 2014 Elsevier Ltd. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kruegel, Florian UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-419879
DOI:	10.1016/j.na.2014.08.019
Journal or Publication Title:	Nonlinear Anal.-Theory Methods Appl.
Volume:	112
Page Range:	S. 165 - 181
Date:	2015
Publisher:	PERGAMON-ELSEVIER SCIENCE LTD
Place of Publication:	OXFORD
ISSN:	1873-5215
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language VARIATIONAL INTEGRALS; EQUATION; MINIMA Multiple languages Mathematics, Applied; Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/41987