Geodesic
Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 3, pp. 484-502

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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,Du)=0 in 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.

DOI : 10.1051/cocv:2007021
Classification : 70H20, 49L25, 35B05
Keywords: Hamilton-Jacobi equations, sub-riemannian metric, viscosity solution, comparison principle 
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     author = {Cutr{\`\i}, Alessandra and Lio, Francesca Da},
     title = {Comparison and existence results for evolutive non-coercive first-order {Hamilton-Jacobi} equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {484--502},
     publisher = {EDP-Sciences},
     volume = {13},
     number = {3},
     year = {2007},
     doi = {10.1051/cocv:2007021},
     mrnumber = {2329172},
     zbl = {1125.70013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007021/}
}
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Cutrì, Alessandra; Lio, Francesca Da. Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 3, pp. 484-502. doi: 10.1051/cocv:2007021

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