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

TL;DR

This paper studies radially symmetric minimizers of a p-Ginzburg-Landau energy in 2D, proving their existence, uniqueness, monotonicity, concavity, stability, and analyzing their behavior as p approaches infinity.

Contribution

It establishes the existence, uniqueness, and stability of radially symmetric minimizers for the p-Ginzburg-Landau energy, including their asymptotic analysis as p increases.

Findings

Unique radially symmetric minimizer exists for each p.

Minimizer's modulus is monotone increasing and concave.

Minimizer is locally stable for p in (2,4].

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 $(2,4]$.