Sobolev mappings and variational integrals, spring 2013
SOBOLEV MAPPINGS and VARIATIONAL INTEGRALS in GEOMETRIC FUNCTION THEORY, spring 2013
Lecturer
Scope
5 cu.
Type
Advanced studies
In great part, these lectures echo recent advances of the variational approach to Geometric Function Theory (GFT), with applied disciplines in mind. We shall provide an in-depth analysis of the concept of energy-minimal deformations (predominantly, traction free boundary value problems in dimension 2) to gain insights into new phenomena encountered in the Calculus of Variations, nonlinear elasticity, material science, and so forth. Analysis of mappings between ring domains leads us to the Collapsing Phenomenon and the Nitsche Conjecture, a charming connection with minimal surfaces. As we seek greater knowledge about the energy-minimal deformations the questions about Sobolev homeomorphisms and their limits become ever more quintessential. In fact the weak and strong limits of Sobolev homeomorphisms will turn out to be the same.
Heart-felt welcome to everybody,
Tadeusz Iwaniec
FiDiPro, Helsinki University
Prerequisites
I will assume basic knowledge of measure theory, integration, analytic functions and some functional analysis.
To make these lectures available to students whose mathematical knowledge may be limited, every effort will be made to reduce to a minimum the technical details and mathematical requirements. No prior exposure to these topics is assumed.
Lectures
Weeks 4-9 and 11-18, Monday 14-16 in room DK117.
Easter holiday 28.3.-3.4.
No Lecture on Monday 28.1.2013!
Exams
There will be no exams or exercise sessions held. Instead, students will be evaluated based on their participation on the lectures. You are invited to pursue the exercises given occasionally during the course.
Bibliography
Notes will be provided during the course.