Tadeusz Iwaniec (University of Helsinki, Finland & Syracuse University, USA), Limits of Sobolev homeomorphisms and traction free energy-minimal deformations

Oddział Warszawski Polskiego Towarzystwa Matematycznego, Instytut Matematyczny  Polskiej Akademii Nauk i Międzynarodowe Centrum Matematyczne im. Stefana Banacha
 

W dniu 15 kwietnia 2014 roku (WTOREK) o godz. 16:30 w sali 322, III piętro, w Instytucie Matematycznym PAN, ul. Śniadeckich 8

Prof. dr hab. Tadeusz Iwaniec (University of Helsinki, Finland & Syracuse University, NY,USA)

wygłosi połączony z posiedzeniem Seminarium Geometrycznej Teorii Funkcji i Przekształceń IM PAN

WYKŁAD - KOLOKWIUM
pod tytułem
LIMITS OF SOBOLEV HOMEOMORPHISMS AND TRACTION FREE ENERGY-MINIMAL DEFORMATIONS

Streszczenie wykładu:
As we seek greater knowledge about the energy-minimal deformations in Geometric Function Theory and Nonlinear Hyperelasticity, the questions about Sobolev homeomorphisms and their limits become ever more quintessential.
We shall discuss the following topics:

1. Approximation of Sobolev homeomorphisms with diffeomorphisms
2. Its relevance to the regularity of hyperelastic deformations of neohookean materials (solution of the Ball-Evans Conjecture)
3. p-Harmonic mappings will come into play
4. A quest for diffeomorphic approximation in higher dimensions (J. Milnor's isotopy in the 7-sphere)
5. Weak and strong limits of Sobolev homeomorphisms are the same; interpenetration of matter may occur
6. Monotone Sobolev deformations of planar domains and surfaces (thin plates and films)
7. Existence of traction free minimal deformations (no Lavrentiev Phenomenon)
8. Hopf-Laplace equation. Lipschitz regularity in spite of collapse of domains
9. Nitsche Conjecture; existence of harmonic diffeomorphisms between doubly connected domains.

Theoretical prediction of failure of bodies caused by interpenetration of matter (collapse of domains) is a good motivation that should appeal to Mathematical Analysts and researchers in the Engineering Fields.
                                                                                                                                                                                                                                                     Tadeusz Iwaniec

Przed wykładem, od godz. 16:00, zapraszamy na spotkanie przy kawie i herbacie w sali klubowej IMPAN na IV piętrze.

Serdecznie zapraszamy,

Organizatorzy