Maximum principles for vectorial approximate minimisers on non-convex functionals

Katzourakis, N. I. (2013) Maximum principles for vectorial approximate minimisers on non-convex functionals. Calculus of Variations and Partial Differential Equations, 46 (3-4). pp. 505-522. ISSN 1432-0835 doi: 10.1007/s00526-012-0491-6

Abstract/Summary

We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance compared to results already existing in the literature is that we have dropped the quasiconvexity assumption of the integrand in the gradient term. The lack of weak Lower semicontinuity is compensated by introducing a nonlinear convergence technique, based on the approximation of the projection onto a convex set by reflections and on the invariance of the integrand in the gradient term under the Orthogonal Group. Maximum Principles are implied for the relaxed solution in the case of non-existence of minimizers and for minimizing solutions of the Euler–Lagrange system of PDE.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/33314
Identification Number/DOI	10.1007/s00526-012-0491-6
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Springer-Verlag
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