Electronic Journal of Differential Equations,
Vol. 1995(1995), No. 06, pp. 1-14.

Title: Regularity for Non-Uniformly Elliptic Systems
       and Application to Some Variational Integrals

Authors: F. Leonetti (Univ. di L'Aquila, Italy)
         C. Musciano (Istituto Nazionale di Alta Matematica, Italy) 

Abstract: This paper deals with higher integrability for
minimizers of some variational integrals whose Euler
equation is elliptic but not uniformly elliptic. This
setting is also referred to as elliptic equations with
$p,q$-growth conditions, following Marcellini. 
Higher integrability of minimizers implies the existence of 
second derivatives. This improves on a result by
Acerbi and Fusco concerning the estimate of the
(possibly) singular set of minimizers.

Submitted September 20, 1994. Published June 7, 1995.
Math Subject Classification: 35J60, 49N60.
Key Words: Regularity; weak solutions; minimizers;
           ellipticity; variational integrals.