Smooth solutions of systems of quasilinear parabolic equations

Bensoussan, Alain; Frehse, Jens

doi:10.1051/cocv:2002059

Bensoussan, Alain; Frehse, Jens

ESAIM: Control, Optimisation and Calculus of Variations, Volume 8 (2002), p. 169-193

Abstract

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.

MR 1932949 | Zbl 1078.35022

DOI : https://doi.org/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

@article{COCV_2002__8__169_0,
     author = {Bensoussan, Alain and Frehse, Jens},
     title = {Smooth solutions of systems of quasilinear parabolic equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {8},
     year = {2002},
     pages = {169-193},
     doi = {10.1051/cocv:2002059},
     zbl = {1078.35022},
     mrnumber = {1932949},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2002__8__169_0}
}

Bensoussan, Alain; Frehse, Jens. Smooth solutions of systems of quasilinear parabolic equations. ESAIM: Control, Optimisation and Calculus of Variations, Volume 8 (2002) , pp. 169-193. doi : 10.1051/cocv:2002059. http://www.numdam.org/item/COCV_2002__8__169_0/

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