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arXiv · 1502.02097

Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds and applications

Yazhou Han·Meijun Zhu
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Abstract

In this paper we extend Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds for dimension $n\ne 2$. As one application, we solve a generalized Yamabe problem on locally conforamlly flat manifolds via a new designed energy functional and a new variational approach. Even for the classic Yamabe problem on locally conformally flat manifolds, our approach provides a new and relatively simpler solution.

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Yazhou Han, Meijun Zhu. 2015-02-07. Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds and applications. https://doi.org/10.1016/j.jde.2015.06.032

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