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
Linköpings universitet
Department of Mathematics, Linköpings universitet