We study the Hamilton-Jacobi equation of the minimal time function in a domain which contains the target set. We generalize the results of Clarke and Nour [J. Convex Anal., 2004], where the target set is taken to be a single point. As an application, we give necessary and sufficient conditions for the existence of solutions to eikonal equations.
Keywords: minimal time function, Hamilton-Jacobi equations, viscosity solutions, minimal trajectories, eikonal equations, monotonicity of trajectories, proximal analysis, nonsmooth analysis
@article{COCV_2006__12_1_120_0, author = {Nour, Chadi}, title = {Semigeodesics and the minimal time function}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {120--138}, publisher = {EDP-Sciences}, volume = {12}, number = {1}, year = {2006}, doi = {10.1051/cocv:2005032}, mrnumber = {2192071}, zbl = {1114.49028}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2005032/} }
TY - JOUR AU - Nour, Chadi TI - Semigeodesics and the minimal time function JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2006 SP - 120 EP - 138 VL - 12 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2005032/ DO - 10.1051/cocv:2005032 LA - en ID - COCV_2006__12_1_120_0 ER -
Nour, Chadi. Semigeodesics and the minimal time function. ESAIM: Control, Optimisation and Calculus of Variations, Volume 12 (2006) no. 1, pp. 120-138. doi : 10.1051/cocv:2005032. http://www.numdam.org/articles/10.1051/cocv:2005032/
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