Ausburg University

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.