On fully nonlinear CR invariant equations on the Heisenberg group

Y. Y. Li; D. D. Monticelli

doi:10.1016/j.jde.2011.09.002

On fully nonlinear CR invariant equations on the Heisenberg group

Y. Y. Li, D. D. Monticelli

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this paper we provide a characterization of second order fully nonlinear CR invariant equations on the Heisenberg group, which is the analogue in the CR setting of the result proved in the Euclidean setting by A. Li and the first author in Li and Li (2003) [21]. We also prove a comparison principle for solutions of second order fully nonlinear CR invariant equations defined on bounded domains of the Heisenberg group and a comparison principle for solutions of a family of second order fully nonlinear equations on a punctured ball.

Original language	English (US)
Pages (from-to)	1309-1349
Number of pages	41
Journal	Journal of Differential Equations
Volume	252
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2011.09.002
State	Published - Jan 15 2012

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Keywords

CR geometry
CR invariant equations
Heisenberg group
Sublaplacian

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10.1016/j.jde.2011.09.002

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title = "On fully nonlinear CR invariant equations on the Heisenberg group",

abstract = "In this paper we provide a characterization of second order fully nonlinear CR invariant equations on the Heisenberg group, which is the analogue in the CR setting of the result proved in the Euclidean setting by A. Li and the first author in Li and Li (2003) [21]. We also prove a comparison principle for solutions of second order fully nonlinear CR invariant equations defined on bounded domains of the Heisenberg group and a comparison principle for solutions of a family of second order fully nonlinear equations on a punctured ball.",

keywords = "CR geometry, CR invariant equations, Heisenberg group, Sublaplacian",

author = "Li, {Y. Y.} and Monticelli, {D. D.}",

note = "Funding Information: E-mail addresses: [email protected] (Y.Y. Li), [email protected] (D.D. Monticelli). 1 Partially supported by NSF grant DMS-0701545 and by Program for Changjiang Scholars and Innovative Research Team in University in China. 2 Partially supported by GNAMPA, project “Equazioni differenziali e sistemi dinamici”. Partially supported by MIUR, project “Metodi variazionali e topologici nello studio di fenomeni nonlineari”.",

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AU - Monticelli, D. D.

N1 - Funding Information: E-mail addresses: [email protected] (Y.Y. Li), [email protected] (D.D. Monticelli). 1 Partially supported by NSF grant DMS-0701545 and by Program for Changjiang Scholars and Innovative Research Team in University in China. 2 Partially supported by GNAMPA, project “Equazioni differenziali e sistemi dinamici”. Partially supported by MIUR, project “Metodi variazionali e topologici nello studio di fenomeni nonlineari”.

PY - 2012/1/15

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N2 - In this paper we provide a characterization of second order fully nonlinear CR invariant equations on the Heisenberg group, which is the analogue in the CR setting of the result proved in the Euclidean setting by A. Li and the first author in Li and Li (2003) [21]. We also prove a comparison principle for solutions of second order fully nonlinear CR invariant equations defined on bounded domains of the Heisenberg group and a comparison principle for solutions of a family of second order fully nonlinear equations on a punctured ball.

AB - In this paper we provide a characterization of second order fully nonlinear CR invariant equations on the Heisenberg group, which is the analogue in the CR setting of the result proved in the Euclidean setting by A. Li and the first author in Li and Li (2003) [21]. We also prove a comparison principle for solutions of second order fully nonlinear CR invariant equations defined on bounded domains of the Heisenberg group and a comparison principle for solutions of a family of second order fully nonlinear equations on a punctured ball.

KW - CR geometry

KW - CR invariant equations

KW - Heisenberg group

KW - Sublaplacian

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -

On fully nonlinear CR invariant equations on the Heisenberg group

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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