Local Minimizers of the Ginzburg-Landau Functional with Prescribed Degrees
Journal of Functional Analysis 257 (2009) 1053-1091 We consider, in a smooth bounded multiply connected domain $\dom\subset\R^2$, the Ginzburg-Landau energy $\d E_\v(u)=1/2\int_\dom{|\n u|^2}+\frac{1}{4\v^2}\int_\dom{(1-|u|^2)^2}$ subject to prescribed degree conditions on each component of $\p\dom$...
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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
07.11.2011
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.1111.1571 |
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| Summary: | Journal of Functional Analysis 257 (2009) 1053-1091 We consider, in a smooth bounded multiply connected domain $\dom\subset\R^2$,
the Ginzburg-Landau energy $\d E_\v(u)=1/2\int_\dom{|\n
u|^2}+\frac{1}{4\v^2}\int_\dom{(1-|u|^2)^2}$ subject to prescribed degree
conditions on each component of $\p\dom$. In general, minimal energy maps do
not exist \cite{BeMi1}. When $\dom$ has a single hole, Berlyand and Rybalko
\cite{BeRy1} proved that for small $\v$ local minimizers do exist. We extend
the result in \cite{BeRy1}: $\d E_\v(u)$ has, in domains $\dom$ with $2,3,...$
holes and for small $\v$, local minimizers. Our approach is very similar to the
one in \cite{BeRy1}; the main difference stems in the construction of test
functions with energy control. |
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| DOI: | 10.48550/arxiv.1111.1571 |