Abstract: In this talk, we discuss a lower semicontinuity result for polyconvex functionals along sequences of maps ƒm : Ω ⊂ ℝn → ℝn bounded in W1,n−1. We assume that ƒm are Sobolev homeomorphisms with positive Jacobians det Dƒm > 0 a.e., satisfy the Lusin (N) condition, have a prescribed Dirichlet boundary data, and supm(|Dƒm|n + A(|cofDƒm|) + φ(det Dƒm)) < ∞ where A and φ are positive convex functions with certain growth behavior. We also consider some examples when lower semicontinuity fails under weaker conditions.
Weak lower semicontinuity of polyconvex integrals in case of low Sobolev regularity
30.10.2024 15:00 - 15:45
Organiser:
R. I. Boţ
Location:
HS 2, EG, OMP 1
Verwandte Dateien
- pde_afternoon_2024-10-30.pdf 921 KB