Electron.n. J. Diff. Eqns. Vol. **1993**(1993), No. 3, pp. 1-9.

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Estimates for smooth absolutely minimizing Lipschitz extensions

Lawrence C. Evans

**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_infinity 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 was placed on March 9, 1994. See last page of this article.

Submitted July 20, 1993. Published October 12, 1993.

Math Subject Classification: 35J70, 26A16.

Key Words: Lipschitz extensions, Harnack inequalities.

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Lawrence C. Evans

Department of Mathematics,
University of California,
Berkeley, CA 94720, USA

e-mail: evans@math.berkeley.edu

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