Global minimizers for a p-Ginzburg-Landau-type energy in R2

Yaniv Almog, Leonid Berlyand, Dmitry Golovaty, Itai Shafrir

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Given a p > 2, we prove existence of global minimizers for a p-Ginzburg-Landau-type energy over maps on R2 with degree d = 1 at infinity. For the analogous problem on the half-plane we prove existence of a global minimizer when p is close to 2. The key ingredient of our proof is the degree reduction argument that allows us to construct a map of degree d = 1 from an arbitrary map of degree d > 1 without increasing the p-Ginzburg-Landau energy.

Original languageEnglish (US)
Pages (from-to)2268-2290
Number of pages23
JournalJournal of Functional Analysis
Volume256
Issue number7
DOIs
StatePublished - Apr 1 2009

All Science Journal Classification (ASJC) codes

  • Analysis

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