Monge Solutions for discontinuous Hamiltonians

Ariela Briani and Andrea Davini
Publication type:
Paper in peer-reviewed journals
ESAIM: Control, Optimisation and Calculus of Variations, vol. 11(2), pp. 229-251
We consider an Hamilton-Jacobi equation of the form

 H ( x , D u ) = 0 x ∈ Ω ⊂ ℝ N , ( 1 ) 
 where H(x,p) is assumed Borel measurable and quasi-convex in p. 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 and supersolution, existence and uniqueness for equation ([see full text]) coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also discussed.
    author={Ariela Briani and Andrea Davini },
    title={Monge Solutions for discontinuous Hamiltonians },
    doi={10.1051/cocv:2005004 },
    journal={ESAIM: Control, Optimisation and Calculus of Variations },
    year={2005 },
    volume={11(2) },