Vol. 86, No. 2, 1980

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ISSN: 0030-8730
Biharmonic and polyharmonic principal functions

Lung O. Chung

Vol. 86 (1980), No. 2, 437–445

The biharmonic principal function problem is the construction of a biharmonic function in a space which “imitates” the behavior of a given singularity function. In this paper we first define the notion of a biharmonic operator which clarifies the modes of “imitation.” We then prove the existence and uniqueness theorem of the biharmonic principal function. The theory is a generalization of the harmonic principal functions to the larger family of biharmonic functions. An indication of its application as well as its further generalization to polyharmonic functions is also given.

Mathematical Subject Classification 2000
Primary: 31C12
Received: 11 September 1978
Published: 1 February 1980
Lung O. Chung