Cauchy–Pompeiu representations for higher order elliptic equations in the unit ball

In this paper we consider the Pompeiu operator in the higher dimensional complex unit ball. The explicit form of its iteration is given. The operator is iterated just once leading to some particular solution to an inhomogeneous bianalytic system. We prove the explicit form of this iteration. Moreove...

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Veröffentlicht in:	Advances in pure and applied mathematics (Berlin, Germany) Germany), 2011-05, Vol.2 (2), p.213-236
Hauptverfasser:	Du, Chunye, Liu, Hua
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Sprache:	eng
Schlagworte:	higher order complex partial differential equation pluriharmonic system Pompeiu formula
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creator	Du, Chunye Liu, Hua
description	In this paper we consider the Pompeiu operator in the higher dimensional complex unit ball. The explicit form of its iteration is given. The operator is iterated just once leading to some particular solution to an inhomogeneous bianalytic system. We prove the explicit form of this iteration. Moreover, some further properties, e.g., the kernel space, of the Pompeiu operator are discussed, which gives an application to the pluriharmonic differential system.
doi_str_mv	10.1515/apam.2010.041
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subjects	higher order complex partial differential equation pluriharmonic system Pompeiu formula
title	Cauchy–Pompeiu representations for higher order elliptic equations in the unit ball
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