Nonlocal Variational Principles with Variable Growth
This paper is concerned with the functional J defined by J(u)=∫Ω×ΩW(x,y,∇u(x),∇u(y))dx dy, where Ω⊂ℝN is a regular open bounded set and W is a real-valued function with variable growth. After discussing the theory of Young measures in variable exponent Sobolev spaces, we study the weak lower semicon...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/435247 |
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| _version_ | 1832548144622075904 |
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| author | Yongqiang Fu Miaomiao Yang |
| author_facet | Yongqiang Fu Miaomiao Yang |
| author_sort | Yongqiang Fu |
| collection | DOAJ |
| description | This paper is concerned with the functional J defined by J(u)=∫Ω×ΩW(x,y,∇u(x),∇u(y))dx dy, where Ω⊂ℝN is a regular open bounded set and W is a real-valued function with variable growth. After discussing the theory of Young measures in variable exponent Sobolev spaces, we study the weak lower semicontinuity and relaxation of J. |
| format | Article |
| id | doaj-art-b0aa2291c3a54604bad0a79bd854558d |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-b0aa2291c3a54604bad0a79bd854558d2025-02-03T06:42:06ZengWileyJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/435247435247Nonlocal Variational Principles with Variable GrowthYongqiang Fu0Miaomiao Yang1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaThis paper is concerned with the functional J defined by J(u)=∫Ω×ΩW(x,y,∇u(x),∇u(y))dx dy, where Ω⊂ℝN is a regular open bounded set and W is a real-valued function with variable growth. After discussing the theory of Young measures in variable exponent Sobolev spaces, we study the weak lower semicontinuity and relaxation of J.http://dx.doi.org/10.1155/2014/435247 |
| spellingShingle | Yongqiang Fu Miaomiao Yang Nonlocal Variational Principles with Variable Growth Journal of Function Spaces |
| title | Nonlocal Variational Principles with Variable Growth |
| title_full | Nonlocal Variational Principles with Variable Growth |
| title_fullStr | Nonlocal Variational Principles with Variable Growth |
| title_full_unstemmed | Nonlocal Variational Principles with Variable Growth |
| title_short | Nonlocal Variational Principles with Variable Growth |
| title_sort | nonlocal variational principles with variable growth |
| url | http://dx.doi.org/10.1155/2014/435247 |
| work_keys_str_mv | AT yongqiangfu nonlocalvariationalprincipleswithvariablegrowth AT miaomiaoyang nonlocalvariationalprincipleswithvariablegrowth |