H1∩Lp versus C1 Local Minimizers
We show that a local minimizer of Φ in the C1 topology must be a local minimizer in the H1∩Lp topology, under suitable assumptions for the functional Φ=(1/2)∫Ω|∇u|2+(1/p)∫Ω|u|p−∫ΩF(x,u) with supercritical exponent p>2∗=2n/(n−2). This result can be used to establish a solution to the corresponding...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/646145 |
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| author | Yansheng Zhong |
| author_facet | Yansheng Zhong |
| author_sort | Yansheng Zhong |
| collection | DOAJ |
| description | We show that a local minimizer of Φ in the C1 topology must be a local minimizer in the H1∩Lp topology, under suitable assumptions for the functional Φ=(1/2)∫Ω|∇u|2+(1/p)∫Ω|u|p−∫ΩF(x,u) with supercritical exponent p>2∗=2n/(n−2). This result can be used to establish a solution to the corresponding equation admitting sub- and supersolution. Hence, we extend the conclusion proved by Brezis and Nirenberg (1993), the subcritical and critical case. |
| format | Article |
| id | doaj-art-ca5f86fb3d724a43ae9fd79d4121a618 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ca5f86fb3d724a43ae9fd79d4121a6182025-02-03T05:58:14ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/646145646145H1∩Lp versus C1 Local MinimizersYansheng Zhong0Department of Mathematics, Fujian Normal University, Fuzhou 350117, ChinaWe show that a local minimizer of Φ in the C1 topology must be a local minimizer in the H1∩Lp topology, under suitable assumptions for the functional Φ=(1/2)∫Ω|∇u|2+(1/p)∫Ω|u|p−∫ΩF(x,u) with supercritical exponent p>2∗=2n/(n−2). This result can be used to establish a solution to the corresponding equation admitting sub- and supersolution. Hence, we extend the conclusion proved by Brezis and Nirenberg (1993), the subcritical and critical case.http://dx.doi.org/10.1155/2014/646145 |
| spellingShingle | Yansheng Zhong H1∩Lp versus C1 Local Minimizers Abstract and Applied Analysis |
| title | H1∩Lp versus C1 Local Minimizers |
| title_full | H1∩Lp versus C1 Local Minimizers |
| title_fullStr | H1∩Lp versus C1 Local Minimizers |
| title_full_unstemmed | H1∩Lp versus C1 Local Minimizers |
| title_short | H1∩Lp versus C1 Local Minimizers |
| title_sort | h1∩lp versus c1 local minimizers |
| url | http://dx.doi.org/10.1155/2014/646145 |
| work_keys_str_mv | AT yanshengzhong h1lpversusc1localminimizers |