Volume 26, 2020
|Number of page(s)||34|
|Published online||03 September 2020|
Necessary and sufficient conditions for the strong local minimality of C1 extremals on a class of non-smooth domains
Department of Mathematics, Universidad Autónoma Metropolitana,
Av. San Rafael Atlixco 186,
Mexico City, Mexico.
2 Department of Mathematics, University of Sussex, Pevensey 2 Building, Falmer, Brighton, BN1 9QH, UK.
* Corresponing author: firstname.lastname@example.org
Accepted: 2 April 2019
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 C1 extremals defined on this class of non-smooth domains. The sufficiency result presented here thus extends the seminal theorem by Grabovsky and Mengesha (2009), where smoothness assumptions are made on the boundary.
Mathematics Subject Classification: 35J50 / 35J60 / 49K10 / 49K20
Key words: Quasiconvexity at the boundary / cones, non-smooth domains / sufficient conditions / strong local minimiser
© EDP Sciences, SMAI 2020
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