Calculus of Variations and Geometric Measure Theory

Constructing diffeomorphisms and homeomorphisms with prescribed derivative

Piotr Hajłasz

created by scharrer on 29 Jul 2024
modified on 30 Jul 2024

18 sep 2024 -- 13:30   [open in google calendar]

Agenda: Get-together (30 min), presentation Piotr Hajłasz (60 min), questions and discussions (30 min).

Registration required for new participants. Please go to our seminar website (allow one work day for processing).

Abstract.

In the talk I will prove that for any measurable mapping $T$ into the space of matrices with positive determinant, there is a diffeomorphism whose derivative equals $T$ outside a set of measure less than $\varepsilon$. Using this fact I will prove that for any measurable mapping $T$ into the space of matrices with non-zero determinant (with no sign restriction), there is an almost everywhere approximately differentiable homeomorphism whose derivative equals $T$ almost everywhere. The talk is based on my joint work with P. Goldstein and Z. Grochulska.