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.