Hardy inequalities on Riemannian manifolds and applications
By L. D’Ambrosio, Serena Dipierro. 2012
103 citations recorded by the source corpus.
We prove a simple sufficient criteria to obtain some Hardy inequalities on Riemannian manifolds related to quasilinear second-order differential operator $\Delta_{p}u := \Div(\abs{\nabla u}^{p-2}\nabla u)$. Namely, if $\rho$ is a nonnegative weight such that $-\Delta_{p}\rho\geq0$, then the Hardy inequality $$c\int_{M}\frac{\abs{u}^{p}}{\rho^{p}}\abs{\nabla \rho}^{p} dv_{g} \leq \int_{M}\abs{\nabla u}^{p} dv_{g}, \quad u\in\Cinfinito_{0}(M)$$ holds. We show concrete examples specializing the function $\rho$.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/edfb6d940541f8188ab71b4902d95c502750d44a
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In Applied Mathematics
- D. Ganguly
- Alexandru Kristály
- Elvise Berchio
- G. Grillo
- Juan Luis V'azquez
- Qiaohua Yang
- Guozhen Lu
- M. Porzio
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Sharp uncertainty principles on Riemannian manifolds: the influence of curvature (2013, background): “n complete, non-compact Riemannian manifolds. As a source of inspiration, the latter work initiated a systematic study of the uncertainty principles on Riemannian manifolds by D’Ambrosio and Dipierro [9], do Carmo and Xia [10], Erb [11], Kombe and Ozaydin [19, 20], Xia [29], Yang, Su¨ and Kong [30],”
- Sharp Poincar\'e-Hardy and Poincar\'e-Rellich inequalities on the hyperbolic space (2015, background): “ce, whereas ∇g,dvg now indicate the Riemannian gradient and measure. Notice that the constant (N−2)2/4 coincides with its optimal Euclidean counterpart. Further results are given in the recent papers [14, 26, 40]. On the other hand Cartan-Hadamard manifolds whose sectional curvatures are bounded abo”