# Regularity of infty-harmonic functions in dimension two

## Luigi De Pascale (Dipartimento di Matematica ed Informatica "U. Dini" (Firenze) )

created by alberti on 22 Nov 2004

24 nov 2004

Abstract.

seminario di calcolo delle variazioni.

when: Wednesday, November 24, at 5.30 pm

where: Dipartimento di Matematica, sala delle riunioni

who: Luigi De Pascale (Università di Pisa)

title: Regularity of infty-harmonic functions in dimension two

abstract: This talk consists of two part of about 45 minuts each. In the first one, I will recall the definition and main properties of infty-harmonic functions. Following a paper by Crandall, Evans and Gariepy, I will show that all blow-ups of such a function at a given point are affine (even though not necessarily the same). In the second part of this talk I will show that in dimension two there is only one blow-up, which implies that every infty-harmonic function on the plane is of class $C^1$ (this result has been proved in a recent paper by O. Savin).

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