Necessary and sufficient conditions for the strong local minimality of C^1 extremals on a class of non-smooth domains

Campos Cordero, Judith and Koumatos, Konstantinos (2019) Necessary and sufficient conditions for the strong local minimality of C^1 extremals on a class of non-smooth domains. ESAIM: Control, Optimisation and Calculus of Variations. ISSN 1292-8119 (Accepted)

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Abstract

Motivated by applications in materials science, a set of quasiconvexity at the boundary conditions is introduced for domains that are locally diffeomorphic to cones. These conditions are shown to be necessary for strong local minimisers in the vectorial Calculus of Variations and a quasiconvexity-based sufficiency theorem is established for C^1 extremals defined on this class of non-smooth domains. The sufficiency result presented here thus extends the seminal theorem by Grabovsky & Mengesha (2009), where smoothness assumptions are made on the boundary.

Item Type: Article
Additional Information: Publisher pDF also permitted from publication. CH 29/4/19
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Konstantinos Koumatos
Date Deposited: 29 Apr 2019 15:03
Last Modified: 01 Jul 2019 15:47
URI: http://sro.sussex.ac.uk/id/eprint/83337

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