Radially symmetric minimizers for a $p$-Ginzburg Landau type energy in $\R^2$

Details Radially symmetric minimizers for a $p$-Ginzburg Landau type energy in $\R^2$ Radially symmetric minimizers for a $p$-Ginzburg Landau type energy in $\R^2$

2010-11-10

arxiv.org/abs/1011.2412v2

Mathematics

Analysis of PDEs

31 pages. Calc. Var. PDE (to appear)

Scientific paper

We consider the minimization of a p-Ginzburg-Landau energy functional over the class of radially symmetric functions of degree one. We prove the existence of a unique minimizer in this class, and show that its modulus is monotone increasing and concave. We also study the asymptotic limit of the minimizers as p \rightarrow \infty. Finally, we prove that the radially symmetric solution is locally stable for $p$ in the interval $(2,4]$.

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