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Optimal decay for solutions of nonlocal semilinear equations with critical exponent in homogeneous groups

Part of: Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  14 May 2024

Nicola Garofalo ,
Annunziata Loiudice  and
Dimiter Vassilev
Nicola Garofalo
Affiliation:
Dipartimento d'Ingegneria Civile e Ambientale (DICEA), Università di Padova, Via Marzolo, 9 - 35131 Padova, Italy (nicola.garofalo@unipd.it)
Annunziata Loiudice
Affiliation:
Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, Via Orabona, 4 - 70125 Bari, Italy (annunziata.loiudice@uniba.it)
Dimiter Vassilev
Affiliation:
Department of Mathematics and Statistics, University of New Mexico, 311 Terrace Street NE, Albuquerque, NM 87106, USA (vassilev@unm.edu)
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Abstract

In this paper, we establish the sharp asymptotic decay of positive solutions of the Yamabe type equation $\mathcal {L}_s u=u^{\frac {Q+2s}{Q-2s}}$ in a homogeneous Lie group, where $\mathcal {L}_s$ represents a suitable pseudodifferential operator modelled on a class of nonlocal operators arising in conformal CR geometry.

Keywords

nonlocal CR Yamabe problemoptimal decay of positive solutionshomogeneous groupsfractional Sobolev inequalityfractional Schrödinger equation

MSC classification

Primary: 35R03: Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.
Secondary: 35R11: Fractional partial differential equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 29
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Copyright
Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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