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1 results

  • Monge solutions for discontinuous Hamiltonians

  • Ariela Briani, Andrea Davini
  • Journal:
    ESAIM: Control, Optimisation and Calculus of Variations / Volume 11 / Issue 2 / April 2005
    Published online by Cambridge University Press:
    15 March 2005, pp. 229-251
    Print publication:
    April 2005

  • We consider an Hamilton-Jacobi equation of the form

 $$ H(x,Du)=0\quad x\in\Omega\subset\mathbb R^N,\qquad\qquad (1) $$ 
where H(x,p) is assumed Borel measurable and quasi-convex inp. The notion of Monge solution, introduced by Newcomb and Su,is adapted to this setting making use of suitable metric devices.We establish the comparison principle for Monge sub andsupersolution, existence and uniqueness for equation ([see full text])coupled with Dirichlet boundary conditions, and a stability result. Therelation among Monge and Lipschitz subsolutions is also discussed.