In this paper we prove a comparison result between semicontinuous viscosity subsolutions and supersolutions to Hamilton-Jacobi equations of the form in where the hamiltonian may be noncoercive in the gradient As a consequence of the comparison result and the Perron’s method we get the existence of a continuous solution of this equation.
Keywords: Hamilton-Jacobi equations, sub-riemannian metric, viscosity solution, comparison principle
@article{COCV_2007__13_3_484_0, 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://www.numdam.org/articles/10.1051/cocv:2007021/} }
TY - JOUR AU - Cutrì, Alessandra AU - Lio, Francesca Da TI - Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2007 SP - 484 EP - 502 VL - 13 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007021/ DO - 10.1051/cocv:2007021 LA - en ID - COCV_2007__13_3_484_0 ER -
%0 Journal Article %A Cutrì, Alessandra %A Lio, Francesca Da %T Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2007 %P 484-502 %V 13 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2007021/ %R 10.1051/cocv:2007021 %G en %F COCV_2007__13_3_484_0
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, Volume 13 (2007) no. 3, pp. 484-502. doi : 10.1051/cocv:2007021. http://www.numdam.org/articles/10.1051/cocv:2007021/
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