High-order Green Operators on the Disk and the Polydisc
Yang Liu, Zhihua Chen, Yifei Pan
TL;DR
This paper derives explicit formulas for high-order Green operators on the disk and polydisc, providing kernel functions and solutions for high-order PDEs in these domains.
Contribution
It introduces explicit expressions for high-order Green operators and their kernels on the disk and polydisc, enabling direct solutions of related PDEs.
Findings
Explicit formulas for high-order Green operators on the disk and polydisc
Kernel functions of these Green operators are derived
Solutions for linear high-order PDEs in the disk are explicitly expressed
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.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Differential Equations and Numerical Methods · Electromagnetic Scattering and Analysis