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Title: Global higher integrability of minimizers of variational problems with mixed boundary conditions
Authors: Fiaschi, AliceKnees, DorotheeReichelt, Sina
Issue Date: 2011
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik, Volume 1664, ISSN 0946-8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: We consider integral functionals with densities of p-growth, with respect to gradients, on a Lipschitz domain with mixed boundary conditions. The aim of this paper is to prove that, under uniform estimates within certain classes of p-growth and coercivity assumptions on the density, the minimizers are of higher integrability order, meaning that they belong to the space of first order Sobolev functions with an integrability of order p+e for a uniform e >0. The results are applied to a model describing damage evolution in a nonlinear elastic body and to a model for shape memory alloys.
Keywords: Higher integrabilty of gradients of minimizers; p-growth; mixed boundary conditions; damage; uniform Caccioppoli-like inequality
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik

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