This spring school will bring together researchers of international stature as well as graduate students in the fields of harmonic analysis and partial differential equations.

For more information, please contact juha.kinnunentkk.fi

Slides for some talks:

Martell (PDF), Mingione (PDF), Nyström (PDF), Urbano (PDF),

Peter Lindqvist (NTNU, Norway):

The time derivative is not merely fractional for the Evolutionary p-Laplacian Equation

Kaj Nyström (Umeå University, Sweden):

Boundary Harnack inequalities for operators of p-Laplace type with variable coefficients

Xiao Zhong (University of Jyväskylä, Finland):

Quasilinear elliptic equations in the Heisenberg group

Frank Duzaar (University of Erlangen-Nürnberg, Germany):

Boundary regularity for non-linear elliptic and parabolic systems

Loukas Grafakos (University of Missouri at Columbia, U.S.A.):

The Carleson-Hunt theorem

Jose Maria Martell (Consejo Superior de Investigaciones Cientificas, Spain):

Weighted norm inequalities and Rubio de Francia extrapolation

Giuseppe Mingione (University of Parma, Italy):

Towards a non-linear Calderòn-Zygmund theory

Jose Miguel Urbano (CMUC-University of Coimbra, Portugal):

The method of intrinsic scaling: a systematic approach to regularity for degenerate and singular PDEs

All lectures are in the hall K in the main building.

Monday10.15-11 Grafakos I

11.15-12 Duzaar I

14.15-15 Martell I

15.15-16 Nyström

Tuesday10.15-11 Urbano I

11.15-12 Grafakos II

14.15-15 Mingione I

15.15-16 Zhong

Wednesday10.15-11 Grafakos III

11.15-12 Martell II

14.15-15 Duzaar II

15.15-16 Urbano II

16.15-17 Lindqvist

Thursday10.15-11 Mingione II

11.15-12 Duzaar III

14.15-15 Urbano III

15.15-16 Martell III

Friday10.15-11 Mingione III

12.15-13 R.T. Rockafellar (University of Washington, Seattle)

Implicit Functions and Solution Mappings in Variational Analysis

Abstract: In traditional mathematics, problems could generally be posed as solving equations, and the question of how a solution might depend on parameters was answered by the classical implicit function theorem. Nowadays, the concept of a problem is much richer and can involve more than just equations. Problem models in terms of optimization, equilibrium, and variational inequalities are important in many applications, for instance. The same question arises of dependence of solutions on parameters, but finding the answers has been the subject of much research.

In 1980, S.M. Robinson published a powerful theorem about solutions to parameterized variational inequalities which, in particular, could represent the first-order optimality conditions in a nonlinear programming problem dependent on parameters. His result covered much of the classical implicit function theorem, if not quite all, but it went far beyond that in ideas and format. It was a landmark in demonstrating how questions of importance in optimization could breath new life into traditional topics in mathematics.

Advances in variational analysis now allow Robinson's theorem to be extended to "generalized equations" much broader than variational inequalities. His notion of first-order approximations can be utilized in the absence of differentiability in describing the effects of perturbations of the parameters. However, even looser forms of approximation are able to furnish significant information about the behavior of solutions.