Boundary regularity for strong local minimizers and Weierstrass problem

13 October 2016
Judith Campos Cordero
We prove partial regularity up to the boundary for strong local minimizers in the case of non-homogeneous integrands and a full regularity result for Lipschitz extremals with gradients of vanishing mean oscillation. As a consequence, we also establish a sufficiency result for this class of extremals, in connection with Grabovsky-Mengesha theorem (2009), which states that $C^1$ extremals at which the second variation is positive, are strong local minimizers. 
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