We consider an optimal control problem for a system of the form = , with a running cost . We prove an interior sphere property for the level sets of the corresponding value function . From such a property we obtain a semiconcavity result for , as well as perimeter estimates for the attainable sets of a symmetric control system.
Keywords: control theory, interior sphere property, value function, semiconcavity, perimeter
@article{COCV_2009__15_1_102_0, author = {Castelpietra, Marco}, title = {Interior sphere property for level sets of the value function of an exit time problem}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {102--116}, publisher = {EDP-Sciences}, volume = {15}, number = {1}, year = {2009}, doi = {10.1051/cocv:2008018}, mrnumber = {2488570}, zbl = {1155.49024}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv:2008018/} }
TY - JOUR AU - Castelpietra, Marco TI - Interior sphere property for level sets of the value function of an exit time problem JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2009 SP - 102 EP - 116 VL - 15 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2008018/ DO - 10.1051/cocv:2008018 LA - en ID - COCV_2009__15_1_102_0 ER -
%0 Journal Article %A Castelpietra, Marco %T Interior sphere property for level sets of the value function of an exit time problem %J ESAIM: Control, Optimisation and Calculus of Variations %D 2009 %P 102-116 %V 15 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2008018/ %R 10.1051/cocv:2008018 %G en %F COCV_2009__15_1_102_0
Castelpietra, Marco. Interior sphere property for level sets of the value function of an exit time problem. ESAIM: Control, Optimisation and Calculus of Variations, Volume 15 (2009) no. 1, pp. 102-116. doi : 10.1051/cocv:2008018. http://archive.numdam.org/articles/10.1051/cocv:2008018/
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