Variational inequalities for energy functionals with nonstandard growth conditions
We consider the obstacle problem {minimize????????I(u)=?OG(?u)dx??among functions??u:O?Rsuch?that???????u|?O=0??and??u=F??a.e. for a given function F?C2(O¯),F|?O<0 and a bounded Lipschitz domain O in Rn. The growth properties of the convex integrand G are described in terms of a N-function A:[0,8...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | Abstract and Applied Analysis |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S1085337598000438 |
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| Summary: | We consider the obstacle problem {minimize????????I(u)=?OG(?u)dx??among functions??u:O?Rsuch?that???????u|?O=0??and??u=F??a.e. for a given function F?C2(O¯),F|?O<0 and a bounded Lipschitz domain O in Rn. The growth properties of the convex integrand G are described in terms of a N-function A:[0,8)?[0,8) with limt?8¯A(t)t-2<8. If n=3, we prove, under certain assumptions on G,C1,8-partial regularity for the solution to the above obstacle problem. For the special case where A(t)=tln(1+t) we obtain C1,a-partial regularity when n=4. One of the main features of the paper is that we do not require any power growth of G. |
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| ISSN: | 1085-3375 |