2004-Fez conference on Differential Equations and Mechanics.
Electronic Journal of Differential Equations,
Conference 11, 2004, pp. 81-93.

Title: An infinite-harmonic analogue of a Lelong theorem
      and infinite-harmonicity cells

Author: Mohammed Boutaleb (Fac. de Sciences Fes, Maroc)
 
Abstract: 
 We consider the problem of finding a function $f$ in
 the set of $\infty$-harmonic functions,  satisfying 
 $$
 \lim_{w\to \zeta } |\widetilde{f}(w)| =\infty,\quad
 w\in \mathcal{H}(D),\quad \zeta \in \partial \mathcal{H}(D)
 $$
 and being a solution to the quasi-linear parabolic equation
 $$
 u_x^2u_{xx}+2u_xu_yu_{xy}+u_y^2u_{yy}=0\quad \hbox{in } D\subset
 \mathbb{R}^2\,,
 $$
 where $D$ is a simply connected plane domain,
 $\mathcal{H}(D)\subset \mathbb{C}^2$
 is the harmonicity cell of $D$, and $\widetilde{f}$ is the holomorphic
 extension of $f$.
 As an application, we show a $p$-harmonic behaviour of the modulus of the
 velocity of an arbitrary stationary plane flow near an extreme point of the
 profile.

Published October 15, 2004.
Math Subject Classifications: 31A30, 31B30, 35J30.
Key Words: Infinite-harmonic functions;  holomorphic extension; 
harmonicity cells;  p-Laplace equation;  stationary plane flow.