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Nondegeneracy of the bubble for the critical p-Laplace equation

Part of: Partial differential equations Elliptic equations and systems

Published online by Cambridge University Press:  20 February 2020

Angela Pistoia  and
Giusi Vaira
Angela Pistoia
Affiliation:
Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma, Via Scarpa 16, Roma00161, Italy ([email protected])
Giusi Vaira
Affiliation:
Dipartimento di Matematica e Fisica, Università degli studi della Campania ‘Luigi Vanvitelli’’, Viale Lincoln 5, Caserta81100, Italy ([email protected])
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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.

MSC classification

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B33: Critical exponents 35J20: Variational methods for second-order elliptic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 1 , February 2021 , pp. 151 - 168
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Copyright
Copyright © The Author(s) 2020. Published by The Royal Society of Edinburgh

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