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arXiv · 1903.11011

Nondegeneracy of the bubble for the critical p-Laplace equation

Angela Pistoia·Giusi Vaira
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Abstract

We prove the non-degeneracy of the extremals of the Sobolev inequality $$\int\limits_{\mathbb R^N}|\nabla u|^pdx\ge \mathcal S_p\int\limits_{\mathbb R^N}|u|^{Np\over N-p}dx,\ u\in \mathcal D^{1,p}(\mathbb R^N)$$ when $1<p<N,$ as solutions of a critical quasilinear equation involving the $p-$Laplacian.

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Angela Pistoia, Giusi Vaira. 2019-11-11. Nondegeneracy of the bubble for the critical p-Laplace equation. https://doi.org/10.1017/prm.2020.7

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