Potential theory and applications in a constructive method for finding critical points of Ginzburg--Landau type equations
type: Item
instance of: scholarly article
title: Potential theory and applications in a constructive method for finding critical points of Ginzburg--Landau type equations
zbMATH Open document ID: 1158.47064
author: Parimah Kazemi
author: J. W. Neuberger
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2008-09-10T00:00:00Z
review text: Let \(H_1\) and \(H_2\) two Hilbert spaces with \(H_1\) dense in \(H_2\), \(H_1\subset H_2\), \(\| x\|_{H_2}\leq\| x\|_{H_1}\). The authors define the transformation \(M : H_2\to H_1\) by \[ (x,y)_{H_2}= (x, My)_{H_1}\quad\forall x\in H_1,\;y\in H_2, \] and prove that \(M^{-1}\) exists, \(M\) has square roots \(\sqrt{M}: H_2\to H_2\), \(\sqrt{M}_{H_1}: H_1\to H_1\), the range of \(\sqrt{M}\) is \(H_1\) and that \(M:H_2\to H_2\) is compact if \(M:H_2\to H_1\) is compact. The authors use their general results to obtain critical points of some energy functionals of Ginzburg--Landau type.
reviewed by: Josef Wloka
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 58E99
zbMATH DE Number: 5324026
MaRDI profile type: Publication
full work available at URL: j.na.2008.02.074
OpenAlex ID: W2040523644
cites work: Q4073917
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DOI: 10.1016/J.NA.2008.02.074
description: scientific article; zbMATH DE number 5324026