Geodesic
Smooth solutions of systems of quasilinear parabolic equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 169-193

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We consider in this article diagonal parabolic systems arising in the context of stochastic differential games. We address the issue of finding smooth solutions of the system. Such a regularity result is extremely important to derive an optimal feedback proving the existence of a Nash point of a certain class of stochastic differential games. Unlike in the case of scalar equation, smoothness of solutions is not achieved in general. A special structure of the nonlinear hamiltonian seems to be the adequate one to achieve the regularity property. A key step in the theory is to prove the existence of Hölder solution.

DOI : 10.1051/cocv:2002059
Classification : 35XX, 49XX
Keywords: parabolic equations, quasilinear, game theory, regularity, stochastic optimal control, smallness condition, specific structure, maximum principle, Green function, hamiltonian 
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     author = {Bensoussan, Alain and Frehse, Jens},
     title = {Smooth solutions of systems of quasilinear parabolic equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {169--193},
     publisher = {EDP-Sciences},
     volume = {8},
     year = {2002},
     doi = {10.1051/cocv:2002059},
     mrnumber = {1932949},
     zbl = {1078.35022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002059/}
}
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Bensoussan, Alain; Frehse, Jens. Smooth solutions of systems of quasilinear parabolic equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 169-193. doi: 10.1051/cocv:2002059

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