Nondegeneracy of the bubble for the critical p-Laplace equation. Issue 1 (February 2021)

• Record Type: Journal Article
• Authors: Pistoia, Angela; Vaira, Giusi
• Is Part Of: Proceedings. Volume 151:Issue 1(2021)
• Page Start: 151
• Page End: 168
• Publication Date: 2021-02
• Subjects: 35J60, -- 35B33, -- 35J20; Mathematics -- Periodicals; 510
• DOI: 10.1017/prm.2020.7
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract: We prove the non-degeneracy of the extremals of the Sobolev inequality \[ \int_{\mathbb R^N}|\nabla u|^p\, \rd x\ge \mathcal S_p\int_{\open R^N}|u|^\frac{Np}{N-p}\, \rd x, \quad u\in \mathcal D^{1, p}(\open R^N) \] when 1 < p < N, as solutions of a critical quasilinear equation involving the p -Laplacian.