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Displaying similar documents to “Da Prato-Zabczyk's maximal inequality revisited. I.”

Existence and uniqueness to the Cauchy problem for linear and semilinear parabolic equations with local conditions

Gerardo Rubio (2011)

ESAIM: Proceedings

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We consider the Cauchy problem in ℝ d for a class of semilinear parabolic partial differential equations that arises in some stochastic control problems. We assume that the coefficients are unbounded and locally Lipschitz, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution by approximation with linear parabolic...

Global Carleman estimate for stochastic parabolic equations, and its application

Xu Liu (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper is addressed to proving a new Carleman estimate for stochastic parabolic equations. Compared to the existing Carleman estimate in this respect (see [S. Tang and X. Zhang, 48 (2009) 2191–2216.], Thm. 5.2), one extra gradient term involving in that estimate is eliminated. Also, our improved Carleman estimate is established by virtue of the known Carleman estimate for deterministic parabolic equations. As its application, we prove the existence of insensitizing controls for backward...

Smooth Solutions of systems of quasilinear parabolic equations

Alain Bensoussan, Jens Frehse (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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...