IJPAM: Volume 72, No. 4 (2011)
RELATED TO TRI-LAPLACE EQUATION
Department of Mathematics
Faculty of Science
Chiang Mai, 50290, THAILAND
Abstract. In this paper, we study the operator where is the operator iterated times and is defined by
where is the dimension of the Euclidean space At first we study the elementary solution or the Green function of the operator and then such a solution is related to the solution of the Laplace equation. We found that the relationship of such solutions depending on the condition and k. Finally, we applied the elementary solution finding solution equation where is an unknown function for , is the generalized function, is a positive integer.
Received: June 3, 2011
AMS Subject Classification: generalized function, temper distribution, Laplace equation
Key Words and Phrases: 30Gxx, 35J05
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395