Local stress regularity in scalar non-convex variational problems

Carsten Carstensen, and Stefan Müller
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Submission date: 05. Feb. 2002
Pages: 20
published in: SIAM journal on mathematical analysis, 34 (2002) 2, p. 495-509 (electronic) 
MSC-Numbers: 49J45, 35B65, 35J60
Keywords and phrases: non-convex minimization, regularization, relaxed problem, stress regularity
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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 in with in (from Euler Lagrange equations and smooth lower order terms) belongs to . 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.