Abstract and Applied Analysis
Volume 3 (1998), Issue 1-2, Pages 41-64

Variational inequalities for energy functionals with nonstandard growth conditions

Martin Fuchs1 and Li Gongbao2

1Universität des Saarlandes, Fachbereich 9 Mathematik, Postfach 151150, Saarbrücken D-66041, Germany
2Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, P.O. Box 71010, China

Received 15 September 1997

Copyright © 1998 Martin Fuchs and Li Gongbao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the obstacle problem {minimizeI(u)=ΩG(u)dxamong functionsu:ΩRsuchthatu|Ω=0anduΦa.e. for a given function ΦC2(Ω¯),Φ|Ω<0 and a bounded Lipschitz domain Ω in Rn. The growth properties of the convex integrand G are described in terms of a N-function A:[0,)[0,) with limt¯A(t)t2<. If n3, we prove, under certain assumptions on G,C1,-partial regularity for the solution to the above obstacle problem. For the special case where A(t)=tln(1+t) we obtain C1,α-partial regularity when n4. One of the main features of the paper is that we do not require any power growth of G.