A method for the construction of Green’s functions

Boley, Bruno A.

doi:10.1090/qam/80250

Author: Bruno A. Boley
Journal: Quart. Appl. Math. 14 (1956), 249-257
MSC: Primary 35.0X
DOI: https://doi.org/10.1090/qam/80250
MathSciNet review: 80250
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Abstract: A method is outlined for the determination of the Green’s function associated with any partial differential equation for arbitrary domains. The Green’s function is obtained as the solution of an integral equation. A method of solution of this equation is discussed which yields the Green’s function as the limit of an infinite sequence of functions. Convergence of this sequence is proved for the case of Helmholtz’ equation. An example from the theory of heat conduction is solved in detail.

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