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]**S. Bergman and M. Schiffer,*Kernel functions and elliptic differential equations in mathematical physics*, Academic Press, New York, 1953 MR**0054140****[2]**P. M. Morse and H. Feshbach,*Methods of mathematical physics*, McGraw-Hill, New York, 1953 MR**0059774****[3]**A. E. H. Love,*Mathematical theory of elasticity*, 4th ed., Dover Publications, New York, 1944 MR**0010851****[4]**H. S. Carslaw and J. C. Jaeger,*Conduction of heat in solids*, Clarendon Press, Oxford, 1947 MR**0022294****[5]**R. Courant and D. Hilbert,*Methods of mathematical physics*, Interscience Publishers, New York, 1953 MR**0065391**

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

Article copyright:
© Copyright 1956
American Mathematical Society