ΕΚΔΗΛΩΣΕΙΣ

Σύνδεσμος:meet.google.com/sru-gxoc-gzw

Ημερομηνία: Παρασκευή 14/5/2021

Ώρα: 15:15

Ομιλητής: Νίκος Αλικάκος (ΕΚΠΑ)

Τίτλος: Sharp lower bounds for the vector Allen-Cahn energy and qualitative properties of minimizers

Περίληψη: We study vector minimizers {uε} with energy J(Ω,u) = Integral over Ω of [ε(|∇u|^2)+(1/ε)W(u))dx] where  W > 0 on Rm \ {a1, ..., aN } , m ≥ 1, for bounded domains Ω ⊂ R2 with certain geometrical features and u = gε on ∂Ω. We derive a sharp lower bound of J(Ω,u) (as ε → 0) with two features:

a) it involves half of the gradient and
b) part of the domain Ω.

Based on this we derive very precise (in ε) pointwise estimates up to the boundary for          lim uε = u0 as ε→0

Depending on the geometry of Ω uε exhibits either boundary layers or internal layers.

We do not impose symmetry hypotheses and we do not employ Γ-convergence techniques.

Joint work with Giorgio Fusco.