2002-Fez conference on Partial Differental Equations,
Electron. J. Diff. Eqns., Conf. 09, 2002, pp. 77-92.

A polyharmonic analogue of a Lelong theorem and polyhedric harmonicity cells

Mohamed Boutaleb

We prove a polyharmonic analogue of a Lelong theorem using the topological method presented by Siciak for harmonic functions. Then we establish the harmonicity cells of a union, intersection, and limit of domains of $\mathbb{R}^n$. We also determine explicitly all the extremal points and support hyperplanes of polyhedric harmonicity cells in $\mathbb{C}^2$.

Published December 28, 2002.
Subject classfications: 31A30, 31B30, 35J30.
Key words: Harmonicity cells, polyharmonic functions, extremal points, Lelong transformation.

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Mohamed Boutaleb
Departement de Mathematiques et Informatique
Faculte des Sciences Dhar-Mahraz
B. P. 1796 Atlas, Fes, Maroc
e-mail: mboutalebmoh@yahoo.fr

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