On the Ginzburg-Landau critical field in three dimensions

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dc.creatorFournais, S.
dc.creatorHelffer, B.
dc.date2007-03-14
dc.date.accessioned2026-07-07T07:51:51Z
dc.date.available2026-07-07T07:51:51Z
dc.descriptionWe study the three dimensional Ginzburg-Landau model of superconductivity. Several `natural' definitions of the (third) critical field, $H_{C_3}$, governing the transition from the superconducting state to the normal state, are considered. We analyze the relation between these fields and give conditions as to when they coincide. An interesting part of the analysis is the study of the monotonicity of the ground state energy of the Laplacian, with constant magnetic field and with Neumann (magnetic) boundary condition, in a domain $Ω$. It is proved that the ground state energy is a strictly increasing function of the field strength for sufficiently large fields. As a consequence of our analysis we give an affirmative answer to a conjecture by Pan.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0703047
dc.identifierhttp://arxiv.org/abs/math-ph/0703047
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125668
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.titleOn the Ginzburg-Landau critical field in three dimensions
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