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Scuola Normale Superiore -Pisa October 1988 Local Regularity for Minimizers

Summary: Scuola Normale Superiore - Pisa October 1988
Local Regularity for Minimizers
of non Convex Integrals
E. Acerbi & N. Fusco
1. Introduction
In this paper we study the regularity of minimizers of the functional
I(u) =

f x, u(x), Du(x) dx, (1.1)
where Rn
is open, u : RN
, and f : × RN
× RnN
R is a
continuous function satisfying
|f(x, s, )| L(1 + ||p
with p 2. This problem has been studied under various ellipticity as-
sumptions on f; for the case when f is uniformly strictly convex in ,


Source: Acerbi, Emilio - Dipartimento di Matematica, Universitą degli Studi di Parma


Collections: Mathematics