# 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).