most citedConcentration on minimal submanifolds for a Yamabe type problem

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math.AP2023

Remainder terms of a nonlocal Sobolev inequality1

Shengbing Deng, Xingliang Tian, Minbo Yang +1

In this note we study a nonlocal version of the Sobolev inequality \begin{equation*} \int_{\mathbb{R}^N}|\nabla u|^2 dx \geq S_{HLS}\left(\int_{\mathbb{R}^N}\big(|x|^{-α} \ast u^{2…

math.AP2023

Stability of Hardy-Sobolev inequality involving p-Laplace

Shengbing Deng, Xingliang Tian

This paper is devoted to considering the following Hardy-Sobolev inequality \[ \int_{\mathbb{R}^N}|\nabla u|^p \mathrm{d}x \geq \mathcal{S}_β\left(\int_{\mathbb{R}^N}\frac{|u|^{p^*…

math.AP2014★ 1 cited

Concentration on minimal submanifolds for a Yamabe type problem

Shengbing Deng, Monica Musso, Angela Pistoia

We construct solutions to a Yamabe type problem on a Riemannian manifold M without boundary and of dimension greater than 2, with nonlinearity close to higher critical Sobolev expo…