 
Summary: A Regularity Theorem
for Minimizersof QuasieonvexIntegrals
EMILIO ACERBI & NICOLA Fusco
Communicated by E. GIUST!
Summary
We prove C 1'~ partial regularity for minimizers of functionals with quasi
convex integrand f(x, u, Du) depending on vectorvalued functions u. The inte
grand is required to be twice continuously differentiable in Du, and no assump
tion on the growth of the derivatives off is made: a polynomial growth is required
only on f itself.
Introduction
Consider the functional I(u) = ff(Du(x)) dx, where s is an open subset
t2
of R',
and f: R "N>~.
The regularity of minimizers of I has been widely investigated (see [8] and
its extensive bibliography), but until recently the function f was required to be
convex, which rules out many interesting physical examples (see [2]) and is far
from quasiconvexity (this condition is necessary and sufficient for the semiconti
nuity of I on appropriate Sobolev spaces, see [1], and so it is a fundamental
