Talk
Weak convergence of minors
- Irene Fonseca (CMU + MPI MiS, Leipzig)
Abstract
Using calculus of variations techniques, it is shown that if un ∈ W1,N(Ω;RN) converge to a function u in L1(Ω;RN), where Ω is an open, bounded subset of RN, if the sequence of all minors {M(𝛻un)} is equi-bounded in L1, and if det𝛻un converge to a function f weakly in L1(Ω), then f = det𝛻u a.e. 𝜘 ∈ Ω.
This result was previously obtained by Giaquinta, Modica and Soucek using tools from Geometric Measure Theory, and it is sharp. In particular, for all q ≥ 1, 1 ≤ p < N - 1, for all f ∈ Lq(Ω), and for every u ∈ W1,p(Ω;RN)
This work in collaboration with Jan Malý was initiated during his visit to the Max Planck Institute in March-April 1998.