A method for the construction of Green's functions

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.

**[1]**Stefan Bergman and M. Schiffer,*Kernel functions and elliptic differential equations in mathematical physics*, Academic Press Inc., New York, N. Y., 1953. MR**0054140****[2]**Philip M. Morse and Herman Feshbach,*Methods of theoretical physics. 2 volumes*, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR**0059774****[3]**A. E. H. Love,*A treatise on the Mathematical Theory of Elasticity*, Dover Publications, New York, 1944. Fourth Ed. MR**0010851****[4]**H. S. Carslaw and J. C. Jaeger,*Conduction of Heat in Solids*, Oxford, at the Clarendon Press, 1947. MR**0022294****[5]**R. Courant and D. Hilbert,*Methods of mathematical physics. Vol. I*, Interscience Publishers, Inc., New York, N.Y., 1953. MR**0065391**

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DOI:
https://doi.org/10.1090/qam/80250

Article copyright:
© Copyright 1956
American Mathematical Society