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The irrotational solution of an elliptic differential equation with an unknown coefficient

Published online by Cambridge University Press:  24 October 2008

J. R. cannon  and
J. H. Halton
J. R. cannon
Affiliation:
Brookhaven National Laboratory, Upton, Long Island, New York and University of Colorado, Boulder, Colorado
J. H. Halton
Affiliation:
Brookhaven National Laboratory, Upton, Long Island, New York and University of Colorado, Boulder, Colorado
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Extract

Let G be a bounded region in k-dimensional space, with boundary Γ, such that the Laplace equation,

is uniquely soluble (to within an added constant) under the Neumann boundary conditions

where ∂/∂n denotes outward normal differentiation on Γ, and it is assumed that h is a function in G ∪ ∂, and thus that g is a function on ∂. In what follows, we shall assume certain properties of the solution h: these are all well known (see, for example, Osgood(l) or Courant(2)).

Information

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 3 , July 1963 , pp. 680 - 682
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Osgood, W. F., Lehrbuch der Funktionentheorie (Teubner; Leipzig, 1928).Google Scholar
(2)Courant, R., Partial differential equations: Vol. n of Methods of mathematical physics (Interscience; New York,1962).Google Scholar