 
Summary: REGULARITY RESULTS FOR A CLASS OF QUASICONVEX
FUNCTIONALS WITH NONSTANDARD GROWTH
EMILIO ACERBI AND GIUSEPPE MINGIONE
Abstract. We consider the integral functional
R
f(x, Du) dx under non stan
dard growth assumptions of (p, q)type: namely, we assume that
zp(x)
f(x, z) L(1 + zp(x)
)
for some function p(x) > 1, a condition appearing in several models from math
ematical physics. Under sharp assumptions on the continuous function p(x) we
prove partial regularity of minimizers in the vectorvalued case u : Rn RN ,
allowing for quasiconvex energy densities. This is, to our knowledge, the first
regularity theorem for quasiconvex functionals under non standard growth
conditions.
1. Introduction.
Over the last thirty years great attention was reserved to the study of regularity
of minimizers of integral functionals of the Calculus of Variations of the type
(1.1) F(u, ) :=
