A Function-Theoretic Method for Δ3 + F(x1, x2)u = 0*
Abstract
IN [4] Tjong showed that by means of an integral operator in the style of Bergman it is possible to generate solutions of
Δ3U + F(x1, x2, x3)U = 0 (1)
where F is assumed to be an entire function of the three complex variables. Tjong's operator maps analytic functions of several complex variables into solutions of equation (1).
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Copyright (c) 1974 R. P. Gilbert, D. K. Kukral
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
D. COLTON AND R. P. GILBERT, An Integral Operator Approach to Cauchy's Problem for ^p+2u{x) + F(x)u(x) = 0, SI AM J. Math. Anal, Vol. 2, No. 1, February, 1971, 113-132.
R.P. GILBERT, Function Theoretic Methods in Partial Differential Equations,. Academic Press, New York and London, 1969.
R.P. GILBERT AND C.Y. LO, On the Approximation of Solutions of Elliptic' Partial Differential Equations in Two and Three Dimensions, SI AM J. Math, Anal. Vol. 2, No. 1, February, 1971, 17-30.
B.L. TJONG, Ph. D. Thesis, University of Kentucky, 1968.
D. COLTON, Bergman Operator for Elliptic equations in three independent variables. Bull. Amer. Math. Soc. 77 (1971) 752-756.