## EVENT DETAILS AND ABSTRACT

**Northwestern Nonlinear PDE Conference**
**Title:** Deriving the $L^\infty$ Euler Equation

**Speaker:** Professor Michael Crandall

**Speaker Info:** University of California at Santa Barbara

**Brief Description:**

**Special Note**:

**Abstract:**

We begin with a quick demonstration of a result of G. Aronsson and R.
Jensen that a function whose gradient has minimum $L^\infty$ norm among
all functions with the same Dirichlet data must satisfy the
infinity-Laplace equation. This minimizing property must be enjoyed with
respect to all subdomains of the domain of definition, which is the
notion of ``absolutely minimizing". Moreover, solutions of the
infinity-Laplace equation are characterized by a comparison property with
respect to the ``cone functions" $C(x)=a|x-z|$. We then discuss the case
of more general functionals than the $L^\infty$ norm of the gradient on
the one hand, and what one finds when attempting to generalize the
characterization of infinity-harmonic functions to the $p$-harmonic case
on the other.

**Date:** Sunday, October 06, 2002

**Time:** 11:00am

**Where:** Leverone Hall G40 ( Kellogg )

**Contact Person:** G.-Q. Chen

**Contact email:** gqchen@math.nwu.edu

**Contact Phone:**

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