Σεμινάριο την Παρασκευή 14 Μαΐου2021 στις 15:15: “Sharp lower bounds for the vector Allen-Cahn energy and qualitative properties of minimizers ”, Νικόλαος Αλικάκος, ΕΚΠΑ

Περίληψη: We study vector minimizers {uε} with energy JΩ(u) = ∫Ω (ε/2 |∇ u|2 + 1/εW(u))dx , where W>0 on Rm\{a1,…,aN} , m≥1, for bounded domain Ω⊂R2 with certain geometrical features and u = gε on ∂Ω. We derive a sharp lower bound of JΩ(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]

Πληροφόρίες: http://users.uoa.gr/~nalikako/seminar/

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