EVENT DETAILS AND ABSTRACT

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.