Please use this identifier to cite or link to this item: doi:10.22028/D291-26189
Title: A note on degenerate variational problems with linear growth
Author(s): Bildhauer, Michael
Language: English
Year of Publication: 2001
Free key words: linear growth
degenerate problems
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: Given a class of strictly convex and smooth integrands f with linear growth, we consider the minimization problem \int_{\Omega}f(\nabla u)dx\rightarrow{\normalcolor min} and the dual problem with maximizer \sigma. Although degenerate problems are studied, the validity of the classical duality relation is proved in the following sense: there exists a generalized minimizer u*\in BV(\Omega;\mathbb{R}^{N}) of the original problem such that \sigma(x)=\nabla f(\nabla^{a}u*) holds almost everywhere, where \nabla^{a}u* denotes the absolutely continuous part of \nabla u* with respect to the Lebesgue measure. In particular, this relation is also true in regions of degeneracy, i.e. at points x such that D^{2}f(\nabla^{a}u*(x))=0. As an appliation, we can improve the known regularity results for the dual solution.
Link to this record: urn:nbn:de:bsz:291-scidok-43380
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 30
Date of registration: 22-Nov-2011
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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