期刊
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
卷 57, 期 2-4, 页码 229-241出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/17476933.2011.638715
关键词
Dirichlet problem; Green function; higher order Poisson equation; polyharmonic equation; doubly connected domain
类别
In this article, we investigate the solvability of the Dirichlet problems in ring domains for elliptic linear complex partial differential equations having polyharmonic operators as main parts. First, we give higher order Green functions as fundamental solutions of the homogeneous problems using the iteration of harmonic Green functions for ring domains. Second, we introduce some classes of operators related to Dirichlet problems together with their basic properties. Next, we transform the original problems into equivalent singular integral equations. Finally, solvability of the problems is discussed by defining the adjoint problems and using Fredholm alternative.
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