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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Wiley
1998-01-01
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| Series: | Abstract and Applied Analysis |
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| Online Access: | http://dx.doi.org/10.1155/S1085337598000438 |
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| author | Martin Fuchs Li Gongbao |
| author_facet | Martin Fuchs Li Gongbao |
| author_sort | Martin Fuchs |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-32c6d8e150494858bbd6fa8efdac25b1 |
| institution | Kabale University |
| issn | 1085-3375 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-32c6d8e150494858bbd6fa8efdac25b12025-02-03T05:45:10ZengWileyAbstract and Applied Analysis1085-33751998-01-0131-2416410.1155/S1085337598000438Variational inequalities for energy functionals with nonstandard growth conditionsMartin Fuchs0Li Gongbao1Universität des Saarlandes, Fachbereich 9 Mathematik, Postfach 151150, Saarbrücken D-66041, GermanyWuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, P.O. Box 71010, ChinaWe 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.http://dx.doi.org/10.1155/S1085337598000438Variational inequalitiesnonstandard growthOrlicz-Sobolev spacesregularity theory. |
| spellingShingle | Martin Fuchs Li Gongbao Variational inequalities for energy functionals with nonstandard growth conditions Abstract and Applied Analysis Variational inequalities nonstandard growth Orlicz-Sobolev spaces regularity theory. |
| title | Variational inequalities for energy functionals with nonstandard
growth conditions |
| title_full | Variational inequalities for energy functionals with nonstandard
growth conditions |
| title_fullStr | Variational inequalities for energy functionals with nonstandard
growth conditions |
| title_full_unstemmed | Variational inequalities for energy functionals with nonstandard
growth conditions |
| title_short | Variational inequalities for energy functionals with nonstandard
growth conditions |
| title_sort | variational inequalities for energy functionals with nonstandard growth conditions |
| topic | Variational inequalities nonstandard growth Orlicz-Sobolev spaces regularity theory. |
| url | http://dx.doi.org/10.1155/S1085337598000438 |
| work_keys_str_mv | AT martinfuchs variationalinequalitiesforenergyfunctionalswithnonstandardgrowthconditions AT ligongbao variationalinequalitiesforenergyfunctionalswithnonstandardgrowthconditions |