no. 1
Interior sphere property for level sets of the value function of an exit time problem
ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 102-116

We consider an optimal control problem for a system of the form x ˙ = f(x,u), with a running cost L. We prove an interior sphere property for the level sets of the corresponding value function V. From such a property we obtain a semiconcavity result for V, as well as perimeter estimates for the attainable sets of a symmetric control system.

DOI : 10.1051/cocv:2008018
Classification : 93B03, 49L20, 49L25
Keywords: control theory, interior sphere property, value function, semiconcavity, perimeter 
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     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},
     year = {2009},
     publisher = {EDP Sciences},
     volume = {15},
     number = {1},
     doi = {10.1051/cocv:2008018},
     mrnumber = {2488570},
     zbl = {1155.49024},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/cocv:2008018/}
}
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Castelpietra, Marco. Interior sphere property for level sets of the value function of an exit time problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 102-116. doi: 10.1051/cocv:2008018

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