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1998 Variational inequalities for energy functionals with nonstandard growth conditions
Martin Fuchs, Li Gongbao
Abstr. Appl. Anal. 3(1-2): 41-64 (1998). DOI: 10.1155/S1085337598000438


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.


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Martin Fuchs. Li Gongbao. "Variational inequalities for energy functionals with nonstandard growth conditions." Abstr. Appl. Anal. 3 (1-2) 41 - 64, 1998.


Published: 1998
First available in Project Euclid: 8 April 2003

zbMATH: 0987.49019
MathSciNet: MR1700276
Digital Object Identifier: 10.1155/S1085337598000438

Primary: 35J70 , 49N60
Secondary: 46E35

Keywords: nonstandard growth , Orlicz-Sobolev spaces , regularity theory , variational inequalities

Rights: Copyright © 1998 Hindawi

Vol.3 • No. 1-2 • 1998
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