Resumen de Regularity results for a class of quasiconvex functionals with nonstandard growth

Emilio Acerbi, Giuseppe Mingione

• We consider the integral ftinctional f f (x, Du) dx under non standard growth assumptions of (p, q)-type: namely, we assume that for some function p(x) > 1, a condition appearing in several models from mathematical physics. Under sharp assumptions on the continuous function p (x ) we prove partial regularity of minimizers in the vector-valued case u : R" -~ allowing for quasiconvex energy densities. This is, to our knowledge, the first regularity theorem for quasiconvex functionals under non standard growth conditions