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  • Produktbild: Ginzburg-Landau Vortices
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Band 13

Ginzburg-Landau Vortices

Aus der Reihe Progress in Nonlinear Differential Equations and Their Applications

97,99 €

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

28.03.1994

Verlag

Birkhäuser Boston

Seitenzahl

162

Maße (L/B/H)

23,5/15,5/1,1 cm

Gewicht

286 g

Auflage

1994

Sprache

Englisch

ISBN

978-0-8176-3723-1

Beschreibung

Rezension

"The three authors are well-known excellent specialists in nonlinear functional analysis and partial differential equations and the material presented in the book covers some of their recent and original results. The book is written in a very clear and readable style with many examples."


--ZAA


"...the book gives a very stimulating account of an interesting minimization problem. It can be a fruitful source of ideas for those who work through the material carefully."


--ZAMP

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

28.03.1994

Verlag

Birkhäuser Boston

Seitenzahl

162

Maße (L/B/H)

23,5/15,5/1,1 cm

Gewicht

286 g

Auflage

1994

Sprache

Englisch

ISBN

978-0-8176-3723-1

Herstelleradresse

Springer-Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

Email: GPSR Kontakt

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  • Produktbild: Ginzburg-Landau Vortices
  • Produktbild: Ginzburg-Landau Vortices
  • I. Energy estimates for S1-valued maps.- 1. An auxiliary linear problem.- 2. Variants of Theorem I.1.- 3. S1-valued harmonic maps with prescribed isolated singularities. The canonical harmonic map.- 4. Shrinking holes. Renormalized energy.- II. A lower bound for the energy of S1-valued maps on perforated domains.- III. Some basic estimates for u?.- 1. Estimates when G=BR and g(x)=x/|x|.- 2. An upper bound for E? (u?).- 3. An upper bound for $$ \frac{1}{{{\varepsilon^2}}}{\smallint_G}{\left( {{{\left| {{u_{\varepsilon }}} \right|}^2} - 1} \right)^2} $$.- 4. $$ \left| {{u_e}} \right| \geqslant \frac{1}{2} $$ on “good discs”.- IV. Towards locating the singularities: bad discs and good discs.- 1. A covering argument.- 2. Modifying the bad discs.- V. An upper bound for the energy of u? away from the singularities.- 1. A lower bound for the energy of u? near aj.- 2. Proof of Theorem V.l.- VI. u?n converges: u? is born!.- 1. Proof of Theorem VI.1.- 2. Further properties of u? : singularities have degree one and they are not on the boundary.- VII. u? coincides with THE canonical harmonic map having singularities (aj).- VIII. The configuration (aj) minimizes the renormalized energy W.- 1. The general case.- 2. The vanishing gradient property and its various forms.- 3. Construction of critical points of the renormalized energy.- 4. The case G=B1 and $$ g\left( \theta \right) = {e^{{i\theta }}} $$.- 5. The case G=B1 and $$ g\left( \theta \right) = {e^{{i\theta }}} $$ with d?.- IX. Some additional properties of u?.- 1. The zeroes of u?.- 2. The limit of $$ \left\{ {{E_{\varepsilon }}\left( {{u_{\varepsilon }}} \right) - \pi d\left| {\log \varepsilon } \right|} \right\} $$ as $$ \varepsilon \to 0 $$.- 3. $$ {\smallint_G}{\left| {\nabla \left| {{u_{\varepsilon }}} \right|} \right|^2} $$ remains bounded as $$ \varepsilon \to 0 $$.- 4. The bad discs revisited.- X. Non minimizing solutions of the Ginzburg-Landau equation.- 1. Preliminary estimates; bad discs and good discs.- 2. Splitting $$ \left| {\nabla {v_{\varepsilon }}} \right| $$.- 3. Study of the associated linear problems.- 4. The basic estimates: $$ {\smallint_G}{\left| {\nabla {v_{\varepsilon }}} \right|^2} \leqslant C\left| {\log \;\varepsilon } \right| $$ and $$ {\smallint_G}{\left| {\nabla {v_{\varepsilon }}} \right|^p} \leqslant {C_p} $$ for p