Some \(L^p\)-Hardy and \(L^p\)-Rellich type inequalities with remainder terms. (English) Zbl 1503.26032
Summary: In this paper we obtain some improved \(L^p\)-Hardy and \(L^p\)-Rellich inequalities on bounded domains of Riemannian manifolds. For Cartan-Hadamard manifolds we prove the inequalities with sharp constants and with weights being hyperbolic functions of the Riemannian distance.
MSC:
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
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