Electronic Journal of Differentialx Equations, Vol. 1993(1993), No. 03, pp. 1-9

Title: Estimates for smooth absolutely minimizing Lipschitz extensions

Author: Lawrence C. Evans (Univ. of California, Berkeley, USA)

Abstract: I present some elementary maximum principle arguments,
establishing interior gradient bounds and Harnack inequalities for
both $u$ and $|Du|$, where $u$ is a smooth solution of the degenerate
elliptic PDE 
	$ \Delta_{\infity} u = 0 $. 
These calculations in particular extend to higher dimensions
G. Aronsson's assertion that a nonconstant, smooth solution can have 
no interior critical point.

An addendum to this article was placed on March 9, 1994.

Submitted July 20, 1993. Published October 12, 1993.
Math Subject Classification: 35J70, 26A16.
Key Words: Lipschitz extensions; Harnack inequalities.