Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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.


References [Enhancements On Off] (What's this?)

  • [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

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