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Fundamental solutions and surface distributions

Published online by Cambridge University Press:  20 January 2009

R. A. Adams  and
G. F. Roach
R. A. Adams
Affiliation:
Department of Mathematics, The University of British Columbia
G. F. Roach
Affiliation:
Department of Mathematics, The University of British Columbia
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When studying the solutions of elliptic boundary value problems in a bounded, smoothly bounded domain D⊂Rn we often encounter the formula

where u(x)∈C2(D)∩C′() is a solution of the second order self-adjoint elliptic equation

and denotes differentiation along the inward normal to ∂D at x∈∂D.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 16 , Issue 3 , June 1969 , pp. 255 - 257
Copyright
Copyright © Edinburgh Mathematical Society 1969

References

REFERENCES

(1)Courant, R. and Hilbert, D.Methods of Mathematical Physics, Vol. II (Interscience, New York, 1962).Google Scholar
(2)Gel'Fand, I. M. and Shilov, G. E.Generalised Functions, Vol. I (Academic Press, 1964).Google Scholar
(3)Schwartz, L.Theorie des distributions (Hermann et Cié, Paris, 1950).Google Scholar