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

Yaniv Almog; Leonid Berlyand; Dmitry Golovaty; Itai Shafrir

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arXiv · 1011.2412

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

Yaniv Almog·Leonid Berlyand·Dmitry Golovaty·Itai Shafrir

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Abstract

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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Yaniv Almog, Leonid Berlyand, Dmitry Golovaty, Itai Shafrir. 2010-12-30. Radially symmetric minimizers for a $p$-Ginzburg Landau type energy in $\R^2$. https://arxiv.org/abs/1011.2412

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