In this paper we provide a complete characterization of fully nonlinear conformally invariant differential operators of any integer order on {$\bold{R}^n$}, which extends the result proved for operators of the second order by A. Li and the first author in Li and Li (2003) [1]. In particular we prove existence and uniqueness of a family of tensors (suitably invariant under Möbius transformations) which are the basic building blocks that appear in the definition of all conformally invariant differential operators on {$\bold{R}^n$}. We also explicitly compute the tensors that are related to operators of order up to four.

On conformally invariant equations on {$\bold{R}^n$} / Y. Li, P. Mastrolia, D.D. Monticelli. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 95(2014 Jan), pp. 339-361. [10.1016/j.na.2013.09.016]

On conformally invariant equations on {$\bold{R}^n$}

P. Mastrolia;D.D. Monticelli
2014-01

Abstract

In this paper we provide a complete characterization of fully nonlinear conformally invariant differential operators of any integer order on {$\bold{R}^n$}, which extends the result proved for operators of the second order by A. Li and the first author in Li and Li (2003) [1]. In particular we prove existence and uniqueness of a family of tensors (suitably invariant under Möbius transformations) which are the basic building blocks that appear in the definition of all conformally invariant differential operators on {$\bold{R}^n$}. We also explicitly compute the tensors that are related to operators of order up to four.
Conformally invariant operators; Elementary conformal tensors; Fully nonlinear higher order equations; Schouten tensor
Settore MAT/05 - Analisi Matematica
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/229733
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