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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
58/1999

Local regularity of solutions of variational problems for the equilibrium configuration of an incompressible, multiphase elastic body

Michael Bildhauer, Martin Fuchs and Gregory A. Seregin

Abstract

We consider a multiphase, incompressible, elastic body with k preferred states whose equilibrium configuration is described in terms of a nonconvex variational problem. We pass to a suitable relaxed variational integral whose solution has the meaning of the strain tensor and also study the associated dual problem for the stresses. At first we show that the strain tensor is smooth near any point of strict J1m-quasiconvexity of the relaxed integrand. Then we use this result to get regularity of the stress tensor on the union of pure phases at least in the two-dimensional case.

Received:
Sep 27, 1999
Published:
Sep 27, 1999
MSC Codes:
49N60, 73C05, 73V25, 73G05

Related publications

inJournal
2001 Repository Open Access
Michael Bildhauer, Martin Fuchs and Gregory A. Seregin

Local regularity of solutions of variational problems for the equilibrium configuration of an incompressible, multiphase elastic body

In: Nonlinear differential equations and applications, 8 (2001) 1, pp. 53-81