Видеотека: P. Mironescu, Ginzburg--Landau energy with prescribed degrees

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Шестая международная конференция по дифференциальным и функционально-дифференциальным уравнениям DFDE-2011 19 августа 2011 г. 10:55, г. Москва

Ginzburg–Landau energy with prescribed degrees P. Mironescu Université Claude Bernard Lyon 1, Lyon, France
Аннотация: We consider the simplified Ginzburg–Landau energy $\frac12\int_\Omega\|\nabla u\|^2+\frac1{(4\varepsilon)^2}\int_\Omega(1-\|u\|^2)^2$. Here, $\Omega$ is a domain in $\mathbb R^2$ and $u$ is complex-valued. On $\partial\Omega$, we prescribe $\|u\|=1$ and the winding numbers of $u$. This is one of the simplest models of critical equation leading to non-scalar bubbles. I will discuss existence/nonexistence results for minimizers/critical points. The talk is based on results of Berlyand, Dos Santos, Farina, Golovaty, Rybalko, and the lecturer. Язык доклада: английский