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April  2011, 29(2): 453-466. doi: 10.3934/dcds.2011.29.453

Semiconcavity of the value function for a class of differential inclusions

1. 

Dipartimento di Matematica, Via della Ricerca Scientifica 1, Università di Roma 'Tor Vergata’, 00133 Roma, Italy

2. 

Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803-4918, United States

Received  September 2009 Revised  March 2010 Published  October 2010

We provide intrinsic sufficient conditions on a multifunction $F$ and endpoint data φ so that the value function associated to the Mayer problem is semiconcave.
Citation: Piermarco Cannarsa, Peter R. Wolenski. Semiconcavity of the value function for a class of differential inclusions. Discrete and Continuous Dynamical Systems, 2011, 29 (2) : 453-466. doi: 10.3934/dcds.2011.29.453
References:
[1]

J.-P. Aubin and H. Frankowska, "Set-Valued Analysis," Birkhäuser, Boston, 1990.

[2]

P. Cannarsa and H. Frankowska, Some characterizations of optimal trajectories in control theory, SIAM J. Control Optim., 29 (1991), 1322-1347. doi: doi:10.1137/0329068.

[3]

P. Cannarsa and C. Sinestrari, "Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control," Birkhäuser, Boston, 2004.

[4]

F. H. Clarke, "Optimization and Nonsmooth Analysis," Wiley, New York, 1983.

[5]

F. H. Clarke, "Necessary Conditions in Dynamic Optimization," Memoir of the American Mathematical Society, 816, 2005.

[6]

F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, and P. R. Wolenski, "Nonsmooth Analysis and Control Theory," Springer, New York, 1998.

[7]

A. Ornelas, Parametrization of Carathéodory multifunctions, Rend. Sem. Mat. Univ. Padova, 83 (1990), 33-44.

[8]

C. Knuckles and P. R. Wolenski, $C^1$ selections of multifunctions in one dimension, Real Analysis Exchange, 22 (1997), 655-676.

[9]

A. Pliś, Accessible sets in control theory, in "International Conference on Differential Equations" (Los Angeles, 1974), Academic Press, (1975), 646-650.

[10]

R. T. Rockafellar and R. Wets, "Variational Analysis," Springer-Verlag, Berlin Heidelberg, 1998. doi: doi:10.1007/978-3-642-02431-3.

show all references

References:
[1]

J.-P. Aubin and H. Frankowska, "Set-Valued Analysis," Birkhäuser, Boston, 1990.

[2]

P. Cannarsa and H. Frankowska, Some characterizations of optimal trajectories in control theory, SIAM J. Control Optim., 29 (1991), 1322-1347. doi: doi:10.1137/0329068.

[3]

P. Cannarsa and C. Sinestrari, "Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control," Birkhäuser, Boston, 2004.

[4]

F. H. Clarke, "Optimization and Nonsmooth Analysis," Wiley, New York, 1983.

[5]

F. H. Clarke, "Necessary Conditions in Dynamic Optimization," Memoir of the American Mathematical Society, 816, 2005.

[6]

F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, and P. R. Wolenski, "Nonsmooth Analysis and Control Theory," Springer, New York, 1998.

[7]

A. Ornelas, Parametrization of Carathéodory multifunctions, Rend. Sem. Mat. Univ. Padova, 83 (1990), 33-44.

[8]

C. Knuckles and P. R. Wolenski, $C^1$ selections of multifunctions in one dimension, Real Analysis Exchange, 22 (1997), 655-676.

[9]

A. Pliś, Accessible sets in control theory, in "International Conference on Differential Equations" (Los Angeles, 1974), Academic Press, (1975), 646-650.

[10]

R. T. Rockafellar and R. Wets, "Variational Analysis," Springer-Verlag, Berlin Heidelberg, 1998. doi: doi:10.1007/978-3-642-02431-3.

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