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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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). |
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| ISSN: | 0972-6802 1758-4965 |