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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
9/2002

Local stress regularity in scalar non-convex variational problems

Carsten Carstensen and Stefan Müller

Abstract

Motivated by relaxation in the calculus of variations, this paper addresses convex but not necessarily strictly convex minimization problems. A class of energy functionals is described for which any stress field $\sigma$ in $L^q(\Omega)$ with div $\sigma$ in $ W^{1,p'}(\Omega)$ (from Euler Lagrange equations and smooth lower order terms) belongs to $ W^{1,q}_{loc}$ $(\Omega)$. Applications include the scalar double-well potential, an optimal design problem, a vectorial double-well problem in a compatible case, and Hencky elastoplasticity with hardening. If the energy density depends only on the modulus of the gradient we also show regularity up to the boundary.

Received:
Feb 5, 2002
Published:
Feb 5, 2002
MSC Codes:
49J45, 35B65, 35J60
Keywords:
non-convex minimization, regularization, relaxed problem, stress regularity

Related publications

inJournal
2002 Repository Open Access
Carsten Carstensen and Stefan Müller

Local stress regularity in scalar nonconvex variational problems

In: SIAM journal on mathematical analysis, 34 (2002) 2, 495-509 (electronic)