Methods and Applications of Analysis

Volume 21 (2014)

Number 4

Special issue dedicated to the 60th birthday of Stephen S.-T. Yau: Part II

Guest editors: John Erik Fornæss, Xiaojun Huang, Song-Ying Li, Yat Sun Poon, Wing Shing Wong, and Zhouping Xin

High-order Green operators on the disk and the polydisc

Pages: 441 – 456

DOI: http://dx.doi.org/10.4310/MAA.2014.v21.n4.a3

Authors

Yang Liu (Department of Mathematics, Zhejiang Normal University, Jinhua, China)

Zhihua Chen (Department of Mathematics, Tongji University, Shanghai, China)

Yifei Pan (Department of Mathematical Sciences, Indiana University – Purdue University, Fort Wayne, Indiana, U.S.A.)

Abstract

In this paper, we give the explicit expressions of high-order Green operators on the disk and the polydisc, and hence the kernel functions of high-order Green operators are also presented. As applications, we present the explicit integral expressions of all the solutions for linear high-order partial differential equations in the disk.

Keywords

Green operator, disk, polydisc, linear partial differential equation

2010 Mathematics Subject Classification

32W50

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