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A Hardy Inequality with Remainder Terms in the Heisenberg Group and the Weighted Eigenvalue Problem
Journal of Inequalities and Applications volume 2007, Article number: 032585 (2007)
Based on properties of vector fields, we prove Hardy inequalities with remainder terms in the Heisenberg group and a compact embedding in weighted Sobolev spaces. The best constants in Hardy inequalities are determined. Then we discuss the existence of solutions for the nonlinear eigenvalue problems in the Heisenberg group with weights for the-sub-Laplacian. The asymptotic behaviour, simplicity, and isolation of the first eigenvalue are also considered.
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Dou, J., Niu, P. & Yuan, Z. A Hardy Inequality with Remainder Terms in the Heisenberg Group and the Weighted Eigenvalue Problem. J Inequal Appl 2007, 032585 (2007). https://doi.org/10.1155/2007/32585
- Vector Field
- Asymptotic Behaviour
- Eigenvalue Problem
- Sobolev Space
- Heisenberg Group