Splitting-type variational problems with x-dependent exponents

In this article we prove regularity results for locally bounded minimizers u: R(n) superset of Omega -> R(N) of functionals of the type

integral(Omega) [(1 + vertical bar del(1)u vertical bar(2))(P(x)/2) + (1 + vertical bar del(2)u vertical bar(2))(q(x)/2)] dx,

where p and q are Lipschitz-functions and del u = (del(1)u, del(2)u) is an arbitrary decompositon of the gradient of u. Related functionals are the topic of the paper [IBr3], but the situation here is not covered.