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MiS Preprint

Local stress regularity in scalar non-convex variational problems

Carsten Carstensen and Stefan Müller


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.

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

Related publications

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)