Seminar Friday 14th of May, 15:15: “Sharp lower bounds for the vector Allen-Cahn energy and qualitative properties of minimizers ”, Nicholas Alikakos (National and Kapodistrian University of Athens, Greece)

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Abstract.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]

The seminar is taking place online due to the ongoing coronavirus pandemic. and can be attended via Google Meet by following this link.

For further information you can visit the Applied Analysis and PDEs Seminar website.