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Journal of Function Spaces and Applications
Volume 2012, Article ID 575819, 22 pages
Research Article

Variable Exponent Spaces of Differential Forms on Riemannian Manifold

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 30 May 2012; Accepted 22 July 2012

Academic Editor: Alberto Fiorenza

Copyright © 2012 Yongqiang Fu and Lifeng Guo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 𝑊 0 1 , 𝑝 ( 𝑚 ) ( Λ 𝑘 𝑀 ) .