GREEN’S IDENTITY, FUNDAMENTAL SOLUTION AND DIRICHLET PROBLEM OF THE DIAMOND OPERATOR

B. Chalermpon (Thailand) and A. Kananthai (Thailand)

Received March 21, 2007

References:

[1] F. John, Partial Differential Equations, 4th Edition, Springer-Verlag, New York, 1982. [2] A. Kananthai, On the solution of the n-dimensional diamond operator, Appl. Math. Comput. 88 (1997), 27-37. [3] I. Stakgold, Boundary Value Problems of Mathematical Physics, Volume II, The Macmillan Company, New York, 1968. [4] F. Treves, Basic Linear Partial Differential Equations, Academic Press, New York, 1975. [5] S. E. Trione, On Marcel Riesz’s ultra-hyperbolic kernel, Studies Appl. Math. 79 (1988), 185-191.

Keywords and phrases: Diamond operator, Green’s identity, fundamental solution.