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Relaxed Energies for Harmonic Maps

  • F. Bethuel
  • H. Brezis
  • J. M. Coron
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 4)

Abstract

Let
$$Omega \subset {\mathbb{R}^3}$$
be an open bounded set such that
$$ \partial \Omega $$
is smooth. Set
$$ {H^1}\left( {\Omega ;{S^2}} \right) = \left\{ {u \in {H^1}\left( {\Omega ;{\mathbb{R}^3}} \right);|u\left( x \right)| = 1 a.e.} \right\} $$
and
$$ H_\varphi ^1\left( {\Omega ;{S^2}} \right) = \left\{ {u \in {H^1}\left( {\Omega ;{S^2}} \right);u = \varphi on \partial \Omega } \right\}, $$
where
$$ \varphi :\partial \Omega \to {S^2} $$
is a given boundary data.

Keywords

Liquid Crystal Boundary Data Relaxed Energy Coron Theorem Static Liquid Crystal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • F. Bethuel
    • 1
  • H. Brezis
    • 2
    • 3
  • J. M. Coron
    • 4
  1. 1.CERMA, ENPCLa Courtine Noisy le GrandFrance
  2. 2.Département de MathématiquesUniversité P. et M. CurieParis Cedex 05France
  3. 3.Department of MathematicsRutgers University, Hill CenterNew BrunswickUSA
  4. 4.Département de MathématiquesUniversité Paris-SudOrsay CedexFrance

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