Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations

Alessandra Cutrì; Francesca Da Lio

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 13, Issue: 3, page 484-502
  • ISSN: 1292-8119

Abstract

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In this paper we prove a comparison result between semicontinuous viscosity subsolutions and supersolutions to Hamilton-Jacobi equations of the form u t + H ( x , D u ) = 0 in I R n × ( 0 , T ) where the Hamiltonian H may be noncoercive in the gradient Du. As a consequence of the comparison result and the Perron's method we get the existence of a continuous solution of this equation.

How to cite

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Cutrì, Alessandra, and Da Lio, Francesca. "Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations." ESAIM: Control, Optimisation and Calculus of Variations 13.3 (2007): 484-502. <http://eudml.org/doc/249998>.

@article{Cutrì2007,
abstract = { In this paper we prove a comparison result between semicontinuous viscosity subsolutions and supersolutions to Hamilton-Jacobi equations of the form $u_t+H(x,Du) = 0$ in $\{\rm I\}\!\{\rm R\}^n\times(0,T)$ where the Hamiltonian H may be noncoercive in the gradient Du. As a consequence of the comparison result and the Perron's method we get the existence of a continuous solution of this equation. },
author = {Cutrì, Alessandra, Da Lio, Francesca},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Hamilton-Jacobi equations; sub-Riemannian metric; viscosity solution; comparison principle},
language = {eng},
month = {6},
number = {3},
pages = {484-502},
publisher = {EDP Sciences},
title = {Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations},
url = {http://eudml.org/doc/249998},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Cutrì, Alessandra
AU - Da Lio, Francesca
TI - Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/6//
PB - EDP Sciences
VL - 13
IS - 3
SP - 484
EP - 502
AB - In this paper we prove a comparison result between semicontinuous viscosity subsolutions and supersolutions to Hamilton-Jacobi equations of the form $u_t+H(x,Du) = 0$ in ${\rm I}\!{\rm R}^n\times(0,T)$ where the Hamiltonian H may be noncoercive in the gradient Du. As a consequence of the comparison result and the Perron's method we get the existence of a continuous solution of this equation.
LA - eng
KW - Hamilton-Jacobi equations; sub-Riemannian metric; viscosity solution; comparison principle
UR - http://eudml.org/doc/249998
ER -

References

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