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- Title
Imbedding inequalities for the composite operator in the Sobolev spaces of differential forms.
- Authors
Bi, Hui; Yuli, Sun
- Abstract
We establish the imbedding inequalities for the composition of the homotopy operator and Green's operator in the weighted Sobolev spaces and Orlicz-Sobolev spaces of differential forms. First we prove both the local and global $L^{p}$ estimates for the composite operator acting on differential forms and obtain the boundedness of the composite operator in the weighted $L^{p}$ spaces. Then, we further study the local and global $L^{\phi}$-norm inequalities for the composite operator. As a consequence we obtain the imbedding inequalities in the Orlicz-Sobolev spaces.
- Subjects
DIFFERENTIAL forms; SOBOLEV spaces; CONTINUOUS groups; SOBOLEV gradients; HOMOTOPY equivalences
- Publication
Journal of Inequalities & Applications, 2015, Vol 2015, Issue 1, p1
- ISSN
1025-5834
- Publication type
Article
- DOI
10.1186/s13660-015-0755-8