In this paper we provide a complete characterization of fully nonlinear differential operators of any integer order on $\R^n$, which exhibit conformal invariance of exponential type. In this way we intend to complete the work that we undertook in [Li, Mastrolia, Monticelli, On conformally invariant equations on ${\bf R^n$} (2012, submitted)], where we introduced the family of elementary conformal tensors $\{T_{m,\alpha}^u\}$ in order to describe all fully nonlinear differential operators of any integer order on $\R^n$ which are conformally invariant of degree $\alpha\neq0$. Examples of the differential operators that we study in this paper are those related to the Q--curvature equation on $\R^4$ and to the Gauss equation on $\R^2$.

On conformally invariant equations on ${\bf R^n$}-II. Exponential invariance / Y. Li, P. Mastrolia, D.D. Monticelli. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 75:13(2012), pp. 5194-5211.

On conformally invariant equations on ${\bf R^n$}-II. Exponential invariance

P. Mastrolia
Secondo
;
D.D. Monticelli
Ultimo
2012

Abstract

In this paper we provide a complete characterization of fully nonlinear differential operators of any integer order on $\R^n$, which exhibit conformal invariance of exponential type. In this way we intend to complete the work that we undertook in [Li, Mastrolia, Monticelli, On conformally invariant equations on ${\bf R^n$} (2012, submitted)], where we introduced the family of elementary conformal tensors $\{T_{m,\alpha}^u\}$ in order to describe all fully nonlinear differential operators of any integer order on $\R^n$ which are conformally invariant of degree $\alpha\neq0$. Examples of the differential operators that we study in this paper are those related to the Q--curvature equation on $\R^4$ and to the Gauss equation on $\R^2$.
Conformally invariant operators; Exponential invariance; Fully nonlinear higher order equations; Schouten tensor
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/219377
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