# IJPAM: Volume 72, No. 4 (2011)

ON SOME OPERATOR
RELATED TO TRI-LAPLACE EQUATION

Wanchak Satsanit
Department of Mathematics
Faculty of Science
Maejo University
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.

AMS Subject Classification: generalized function, temper distribution, Laplace equation

Key Words and Phrases: 30Gxx, 35J05