An a priori Campanato type regularity condition for local minimisers in the calculus of variations
Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK. T.J.Dodd@ma.hw.ac.uk
An a priori Campanato type regularity condition is established for a class of W1X local minimisers of the general variational integral where is an open bounded domain, F is of class C2, F is strongly quasi-convex and satisfies the growth condition for a p > 1 and where the corresponding Banach spaces X are the Morrey-Campanato space , µ < n, Campanato space and the space of bounded mean oscillation . The admissible maps are of Sobolev class W1,p, satisfying a Dirichlet boundary condition, and to help clarify the significance of the above result the sufficiency condition for W1BMO local minimisers is extended from Lipschitz maps to this admissible class.
Mathematics Subject Classification: 49N60 / 49K10
Key words: Calculus of variations / local minimiser / partial regularity / strong quasiconvexity / Campanato space / Morrey space / Morrey-Campanato space / space of bounded mean oscillation / extremals / positive second variation
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