Minimization of a quasi-linear Ginzburg–Landau type energy

Authors :: Carmen Perugia
Rejeb Hadiji
Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA)
Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM)
Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)
Dipartimento di Studi Geologici ed Ambientali
Universit a del Sannio
Hadiji, Rejeb
Source :: Nonlinear Analysis: Theory, Methods and Applications, Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2009, 71 (3-4), pp.860--875. ⟨10.1016/j.na.2008.11.078⟩, Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2009, 71 (no 3-4), p. 860-875
Publication Year :: 2009
Publisher :: Elsevier BV, 2009.
Abstract: Let G be a smooth bounded domain in R 2 . Consider the functional E e ( u ) = 1 2 ∫ G ( p 0 + t | x | k | u | l ) | ∇ u | 2 + 1 4 e 2 ∫ G ( 1 − | u | 2 ) 2 on the set H g 1 ( G , C ) = { u ∈ H 1 ( G , C ) ; u = g on ∂ G } where g is a given boundary data with degree d ≥ 0 . In this paper we will study the behavior of minimizers u e of E e and we will estimate the energy E e ( u e ) .

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