Functionals with \(p(x)\) growth (Q1851412)

Some recent results are reported concerning the regularity of local minimizers of functionals \(\int f(x,Du)dx\) with nonstandard growth of \((p,q)\) type, namely \(|z|^p(x) \leq f(x,z) \leq L(1+|z|^p(x)),\) where \(p\) is a continuous function. Under sharp assumptions on the function \(p\), regularity results for the minimizers are proved, both in the scalar and the vectorial case.