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Communications in Mathematical Physics

, Volume 301, Issue 2, pp 383–410 | Cite as

Local Well-Posedness for Membranes in the Light Cone Gauge

  • Paul T. Allen
  • Lars AnderssonEmail author
  • Alvaro Restuccia
Article

Abstract

In this paper we consider the classical initial value problem for the bosonic membrane in light cone gauge. A Hamiltonian reduction gives a system with one constraint, the area preserving constraint. The Hamiltonian evolution equations corresponding to this system, however, fail to be hyperbolic. Making use of the area preserving constraint, an equivalent system of evolution equations is found, which is hyperbolic and has a well-posed initial value problem. We are thus able to solve the initial value problem for the Hamiltonian evolution equations by means of this equivalent system. We furthermore obtain a blowup criterion for the membrane evolution equations, and show, making use of the constraint, that one may achieve improved regularity estimates.

Keywords

Gauge Theory Poisson Bracket Sobolev Inequality Symplectic Structure Class Constraint 
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-Verlag 2010

Authors and Affiliations

  • Paul T. Allen
    • 1
    • 2
  • Lars Andersson
    • 1
    Email author
  • Alvaro Restuccia
    • 3
  1. 1.Albert Einstein InstitutePotsdamGermany
  2. 2.Department of Mathematical SciencesLewis& Clark CollegePortlandUSA
  3. 3.Department of PhysicsSimon Bolivar UniversityCaracasVenezuela

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