Mester, Ágnes and Peter, Ioan Radu and Varga, Csaba (2021) Sufficient criteria for obtaining Hardy inequalities on Finsler manifolds. Mediterranean Journal of Mathematics. pp. 1-22. ISSN 1660-5446 (print); 1660-5454 (online) (In Press)
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Mester, Peter, Varga - Sufficient criteria for obtaining Hardy inequalities on Finsler manifolds (MJOM).pdf Download (482kB) | Preview |
Abstract
We establish Hardy inequalities involving a weight function on complete, not necessarily reversible Finsler manifolds. We prove that the superharmonicity of the weight function provides a sufficient condition to obtain Hardy inequalities. Namely, if ρ is a nonnegative function and −∆ρ≥0 in weak sense, where ∆ is the Finsler-Laplace operator defined by ∆ρ= div(∇ρ), then we obtain the generalization of some Riemannian Hardy inequalities given in D’Ambrosio and Dipierro (2013). By extending the results obtained, we prove a weighted Caccioppoli-type inequality, a Gagliardo-Nirenberg inequality and a Heisenberg-Pauli-Weyl uncertainty principle on complete Finsler manifolds. Furthermore, we present some Hardy inequalities on Finsler-Hadamard manifolds with finite reversibility constant, by defining the weight function with the help of the distance function. Finally, we extend a weighted Hardy-inequality to a class of Finsler manifolds of bounded geometry.
Item Type: | Article |
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Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA74 Analysis / analízis |
Depositing User: | Dr. Alexandru Kristaly |
Date Deposited: | 13 Oct 2020 12:47 |
Last Modified: | 13 Oct 2020 12:47 |
URI: | http://real.mtak.hu/id/eprint/115925 |
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