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- W1708145938 abstract "This paper is devoted to the study of the eigenvalue problems for the Ginzburg-Landau operator in the entire plane <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper R squared> <mml:semantics> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding=application/x-tex>{mathbb {R}}^{2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and in the half plane <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper R Subscript plus Superscript 2> <mml:semantics> <mml:msubsup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>+</mml:mo> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:annotation encoding=application/x-tex>{mathbb {R}}^{2}_{+}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The estimates for the eigenvalues are obtained and the existence of the associate eigenfunctions is proved when <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=c u r l upper A> <mml:semantics> <mml:mrow> <mml:mi>c</mml:mi> <mml:mi>u</mml:mi> <mml:mi>r</mml:mi> <mml:mi>l</mml:mi> <mml:mi>A</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>curl A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a non-zero constant. These results are very useful for estimating the first eigenvalue of the Ginzburg-Landau operator with a gauge-invariant boundary condition in a bounded domain, which is closely related to estimates of the upper critical field in the theory of superconductivity." @default.
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- W1708145938 date "1999-10-06" @default.
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- W1708145938 title "Gauge Invariant Eigenvalue Problems in ℝⁿ and in ℝⁿ₊" @default.
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- W1708145938 doi "https://doi.org/10.1090/s0002-9947-99-02516-7" @default.
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