CUBO A Mathematical Journal Vol.14, N^o02, (43-59). June 2012

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A New proof of the CR Identity and related Topics.

 

Najoua Gamara Ali Ben Ahmed and Aribi Amine

Département de Mathématiques, Faculté des Sciences de Tunis, and El Manar II 2092, Tunis, Tunisia.  email: Najoua.Gamara@fst.rnu.tn email: Ali.Ben.Ahmed@umpa.ens-lyon.fremail: Amine.Aribi@lmpt.univ-tours.fr

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ABSTRACT

In this paper we give a new proof for "the CR Identity" and deduce non existence results of positive solutions for semi-linear boundary value problems on star-shaped domains

where is the sublaplacian of the Heisenberg group , function on a star-shaped and bounded domain.

 

Keywords and Phrases: Analysis on CR manifolds, CR structure, CR Identity, Critical growth, Yamabe like problems.

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RESUMEN

En este artículo presentamos una nueva demostración de la identidad de CR Pohozaev sobre el grupo de Heisenberg y deducimos resultados sobre la no existencia de soluciones positivas para problemas semi-lineales con valores en la frontera sobre dominios estrellados

donde es el sublaplaciano del grupo de Heisenberg Hⁿ, g es una función de clase C¹ sobre un dominio estrellado y acotado .

 

2010 AMS Mathematics Subject Classification: 32V20; 32V05; 35H10; 35B20; 35J60; 22E30; 35B60; 35J65; 35B45.

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Received: April 2011. Revised: September 2011.