Radially symmetric minimizers for a p-Ginzburg Landau type energy in ℝ2

Yaniv Almog; Leonid Berlyand; Dmitry Golovaty; Itai Shafrir

doi:10.1007/s00526-011-0396-9

Radially symmetric minimizers for a p-Ginzburg Landau type energy in ℝ²

Yaniv Almog, Leonid Berlyand, Dmitry Golovaty, Itai Shafrir

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11 Scopus citations

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 → ∞. Finally, we prove that the radially symmetric solution is locally stable for 2 < p ≤ 4.

Original language	English (US)
Pages (from-to)	517-546
Number of pages	30
Journal	Calculus of Variations and Partial Differential Equations
Volume	42
Issue number	3
DOIs	https://doi.org/10.1007/s00526-011-0396-9
State	Published - Nov 2011

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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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 → ∞. Finally, we prove that the radially symmetric solution is locally stable for 2 < p ≤ 4.",

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AB - 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 → ∞. Finally, we prove that the radially symmetric solution is locally stable for 2 < p ≤ 4.

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Radially symmetric minimizers for a p-Ginzburg Landau type energy in ℝ²

Abstract

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