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Uniqueness of solutions of improperly posed problems for singular ultrahyperbolic equations

Published online by Cambridge University Press:  09 April 2009

Eutiquio C. Young
Eutiquio C. Young
Affiliation:
Florida State University, Tallahassee, Florida, U.S.A.
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In [1], Owen gave sufficient conditions for the uniqueness of certain mixed problems having elliptic and hyperbolic nature for the ultrahyperbolic equation. Recently, Diaz and Young [2] has obtained necessary and sufficient conditions for the uniqueness of solutions of the Dirichlet and Neumann problems involving the more general ultrahyperbolic equation The purpose of this paper is to present corresponding uniqueness conditions for the Dirichlet and Neumann problems for the singular ultrahyperbolic equation for all values of the parameter, α −∞ > α > ∞. The symbol Δ denotes the Laplace operator in the variables x1, …, xm, Dj indicates partial differentiation with respect to the variable yj (1 ≧ J ≧ n), and the summation convention is adopted for repeated indices including (iu2), where denotes differentiation with respect to the variable xi.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 1 , August 1974 , pp. 97 - 103
Copyright
Copyright © Australian Mathematical Society 1974

References

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