Please use this identifier to cite or link to this item: doi:10.22028/D291-26190
Title: Relaxation of convex variational problems with linear growth defined on classes of vector-valued functions
Author(s): Bildhauer, Michael
Fuchs, Martin
Language: English
Year of Publication: 2001
Free key words: generalized minimizers
functions of bounded variation
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: For a bounded Lipschitz domain \Omega\subset\mathbb{R}^{n} and a function u_{0}\in W_{1}^{1}(\Omega;\mathbb{R}^{N}) we consider the minimization problem (\mathcal{P}) \int_{\Omega}f(\nabla u)dx\rightarrow\mbox{min in}\: u_{0}+\overset{\text{\textdegree}}{W_{1}^{1}}(\Omega;\mathbb{R}^{N}) where f:\mathbb{R}^{nN}\rightarrow[0,\infty) is a strictly convex integrand. Let \mathcal{M} denote the set of all L^{1}-cluster points of minimizing sequences of problem (\mathcal{P}) coincides with the relaxation based on the notation of the extended Lagrangian, moreover, we prove that the elements u of \mathcal{M}are in one-to-one correspondence with the solutions of the relaxed problems.
Link to this record: urn:nbn:de:bsz:291-scidok-43514
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 33
Date of registration: 22-Nov-2011
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

Files for this record:
File Description SizeFormat 
preprint_33_01.pdf255,63 kBAdobe PDFView/Open

Items in SciDok are protected by copyright, with all rights reserved, unless otherwise indicated.