Hardy inequalities on Riemannian manifolds and applications

  • Lorenzo D'Ambrosio

    Dipartimento di Matematica, via E. Orabona, 4, I-70125, Bari, Italy
  • Serena Dipierro

    SISSA, Sector of Mathematical Analysis, via Bonomea, 265, I-34136, Trieste, Italy

Abstract

We prove a simple sufficient criterion to obtain some Hardy inequalities on Riemannian manifolds related to quasilinear second order differential operator . Namely, if is a nonnegative weight such that , then the Hardy inequality

holds. We show concrete examples specializing the function .

Our approach allows to obtain a characterization of -hyperbolic manifolds as well as other inequalities related to Caccioppoli inequalities, weighted Gagliardo–Nirenberg inequalities, uncertain principle and first order Caffarelli–Kohn–Nirenberg interpolation inequality.

Cite this article

Lorenzo D'Ambrosio, Serena Dipierro, Hardy inequalities on Riemannian manifolds and applications. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 3, pp. 449–475

DOI 10.1016/J.ANIHPC.2013.04.004