Variational inequalities for energy functionals with nonstandardgrowth conditions

Abstract

We consider the obstacle problem urn:x-wiley:10853375:media:aaa495907:aaa495907-math-0001 for a given function and a bounded Lipschitz domain O in R n . The growth properties of the convex integrand G are described in terms of a N ‐function A : [0, 8 )?[0, 8 ) with . If n = 3, we prove, under certain assumptions on G , C 1, 8 ‐partial regularity for the solution to the above obstacle problem. For the special case where A ( t ) = t ln(1 + t ) we obtain C 1, a ‐partial regularity when n = 4. One of the main features of the paper is that we do not require any power growth of G .