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The notion of -stability is defined using the lower Dini directional derivatives and was introduced by the authors in their previous papers. In this paper we prove that the class of -stable functions coincides with the class of C functions. This also solves the question posed by the authors in SIAM J. Control Optim. 45 (1) (2006), pp. 383–387.
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...
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