Variable Exponent Spaces of Differential Forms on Riemannian Manifold
We introduce the Lebesgue space and the exterior Sobolev space for differential forms on Riemannian manifold 𝑀 which are the Lebesgue space and the Sobolev space of functions on 𝑀, respectively, when the degree of differential forms to be zero. After discussing the properties of these spaces, we obt...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/575819 |
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| _version_ | 1832562808665931776 |
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| author | Yongqiang Fu Lifeng Guo |
| author_facet | Yongqiang Fu Lifeng Guo |
| author_sort | Yongqiang Fu |
| collection | DOAJ |
| description | We introduce the Lebesgue space and the exterior Sobolev space for
differential forms on Riemannian manifold 𝑀 which are the Lebesgue space
and the Sobolev space of functions on 𝑀, respectively, when the degree of
differential forms to be zero. After discussing the properties of these spaces, we obtain the existence and uniqueness of weak solution for Dirichlet problems of nonhomogeneous 𝑝(𝑚)-harmonic equations with variable growth in 𝑊01,𝑝(𝑚)(Λ𝑘𝑀). |
| format | Article |
| id | doaj-art-5689be18fa0540809c41d58af2d496e9 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-5689be18fa0540809c41d58af2d496e92025-02-03T01:21:39ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/575819575819Variable Exponent Spaces of Differential Forms on Riemannian ManifoldYongqiang Fu0Lifeng Guo1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaWe introduce the Lebesgue space and the exterior Sobolev space for differential forms on Riemannian manifold 𝑀 which are the Lebesgue space and the Sobolev space of functions on 𝑀, respectively, when the degree of differential forms to be zero. After discussing the properties of these spaces, we obtain the existence and uniqueness of weak solution for Dirichlet problems of nonhomogeneous 𝑝(𝑚)-harmonic equations with variable growth in 𝑊01,𝑝(𝑚)(Λ𝑘𝑀).http://dx.doi.org/10.1155/2012/575819 |
| spellingShingle | Yongqiang Fu Lifeng Guo Variable Exponent Spaces of Differential Forms on Riemannian Manifold Journal of Function Spaces and Applications |
| title | Variable Exponent Spaces of Differential Forms on Riemannian Manifold |
| title_full | Variable Exponent Spaces of Differential Forms on Riemannian Manifold |
| title_fullStr | Variable Exponent Spaces of Differential Forms on Riemannian Manifold |
| title_full_unstemmed | Variable Exponent Spaces of Differential Forms on Riemannian Manifold |
| title_short | Variable Exponent Spaces of Differential Forms on Riemannian Manifold |
| title_sort | variable exponent spaces of differential forms on riemannian manifold |
| url | http://dx.doi.org/10.1155/2012/575819 |
| work_keys_str_mv | AT yongqiangfu variableexponentspacesofdifferentialformsonriemannianmanifold AT lifengguo variableexponentspacesofdifferentialformsonriemannianmanifold |