# Monge solutions for discontinuous hamiltonians

ESAIM: Control, Optimisation and Calculus of Variations (2005)

- Volume: 11, Issue: 2, page 229-251
- ISSN: 1292-8119

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topBriani, Ariela, and Davini, Andrea. "Monge solutions for discontinuous hamiltonians." ESAIM: Control, Optimisation and Calculus of Variations 11.2 (2005): 229-251. <http://eudml.org/doc/245885>.

@article{Briani2005,

abstract = {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 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 (1) coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also discussed.},

author = {Briani, Ariela, Davini, Andrea},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {viscosity solution; lax formula; Finsler metric; Lax formula; fronts in nonhomogeneous media; Monge subsolutions; Monge supersolutions; Dirichlet boundary conditions},

language = {eng},

number = {2},

pages = {229-251},

publisher = {EDP-Sciences},

title = {Monge solutions for discontinuous hamiltonians},

url = {http://eudml.org/doc/245885},

volume = {11},

year = {2005},

}

TY - JOUR

AU - Briani, Ariela

AU - Davini, Andrea

TI - Monge solutions for discontinuous hamiltonians

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2005

PB - EDP-Sciences

VL - 11

IS - 2

SP - 229

EP - 251

AB - 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 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 (1) coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also discussed.

LA - eng

KW - viscosity solution; lax formula; Finsler metric; Lax formula; fronts in nonhomogeneous media; Monge subsolutions; Monge supersolutions; Dirichlet boundary conditions

UR - http://eudml.org/doc/245885

ER -

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