Preprint 9/2002

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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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 formula10 in formula12 with formula14 in formula16 (from Euler Lagrange equations and smooth lower order terms) belongs to formula18formula20. 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.

03.07.2017, 01:40