# Nonlinear problems for $\Delta_p$ and $\Delta$

The conference took place 10-14 August 2009 in Linköping.

The aim of the conference was to cover $p$-harmonic functions, $\infty$-harmonic functions, $p$-parabolic functions, water waves and related subjects such as various types of generalizations including quasiminimizers, the porous media equation and the corresponding theories on metric spaces.

# Lecture series

A major part of the conference was devoted to four series of three lectures each. These series were given by the following speakers:

Michael Crandall (Santa Barbara): The $\infty$-Laplacian and other aspects of $L^\infty$ variational problems
Juha Kinnunen (Helsinki Tech): Superparabolic functions
Olli Martio (Helsinki): Quasiminimizers - definitions, constructions and capacity estimates
John Toland (Bath): Bernoulli free boundaries, Lecture 1, Lecture 2, Lecture 3.

# Invited speakers

The following invited speakers participated in the conference.

Walter Craig (McMaster, Hamilton): Normal forms for surface water waves
Ugo Gianazza (Pavia): Continuity of the Saturation in the Flow of Two Immiscible Fluids in a Porous Medium
Mark Groves (Saarbrücken): Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves
Robert Jensen (Loyola, Chicago): Curvature flow connections with $\Delta_\infty$
Nikolay Kuznetsov (St Petersburg): The Benjamin-Lighthil conjecture for nearcritical values of Bernoulli's constant
Peter Lindqvist (Trondheim): A minimax problem with variable exponent
Kaj Nyström (Umeå): Regularity and Free Boundary Regularity for the p-Laplace Operator in Reifenberg Flat and Ahlfors Regular Domains
Xiao Zhong (Jyväskylä): Regularity of p-harmonic functions in the Heisenberg group

# Short communications

There were about 20 short communications (25 min) in two parallel sessions.

# Social program

There was an excursion on Wednesday afternoon and conference dinners on Tuesday and Thursday.

# Support

We heartly acknowledge the support from the following sources:

European Science Foundation Networking Programme Harmonic and Complex Analysis and Applications HCAA
NordForsk Scandinavian Network Analysis and Applications
Vetenskapsrådet (The Swedish Science Research Council)
Wenner-Gren stiftelserna

# Technical information

The lecture halls have whiteboards. There will also be computers available for the talks and projectors for slides and computers.

The participants will have access to a room with computers, as well as the possibility to connect to the Internet using wireless connections on their own laptops.

# Organizers

Gunnar Aronsson, Anders Björn, Jana Björn, Vladimir Kozlov, Bengt-Ove Turesson and Theresia Roth (secr.).

# Contact email

conf-p-laplace@mai.liu.se

Page responsible: jana.bjorn@liu.se
Last updated: 2015-01-19