On Bellman systems without zero order term in the context of risk sensitive differential games

Alain Bensoussan; Jens Frehse

Displaying similar documents to “On Bellman systems without zero order term in the context of risk sensitive differential games”

Pointwise estimates of nonnegative subsolutions of quasilinear elliptic equations at irregular boundary points

Jan Malý (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let $u$ be a weak solution of a quasilinear elliptic equation of the growth $p$ with a measure right hand term $μ$ . We estimate $u (z)$ at an interior point $z$ of the domain $Ω$ , or an irregular boundary point $z \in \partial Ω$ , in terms of a norm of $u$ , a nonlinear potential of $μ$ and the Wiener integral of $𝐑^{n} ∖ Ω$ . This quantifies the result on necessity of the Wiener criterion.

Hölder regularity for nonhomogeneous elliptic systems with nonlinearity greater than two

Giovanna Idone (2004)

Czechoslovak Mathematical Journal

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Regularity results for elliptic systems of second order quasilinear PDEs with nonlinear growth of order $q > 2$ are proved, extending results of [7] and [10]. In particular Hölder regularity of the solutions is obtained if the dimension $n$ is less than or equal to $q + 2$ .

Regularity results for a class of obstacle problems in Heisenberg groups

Francesco Bigolin (2013)

Applications of Mathematics

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We study regularity results for solutions $u \in H W^{1, p} (Ω)$ to the obstacle problem $\int_{Ω} 𝒜 (x, \nabla_{ℍ} u) \nabla_{ℍ} (v - u) d x \geq 0 \forall v \in 𝒦_{ψ, u} (Ω)$ such that $u \geq ψ$ a.e. in $Ω$ , where $𝒦_{ψ, u} (Ω) = {v \in H W^{1, p} (Ω) : v - u \in H W_{0}^{1, p} (Ω) v \geq ψ a.e. in Ω}$ , in Heisenberg groups $ℍ^{n}$ . In particular, we obtain weak differentiability in the $T$ -direction and horizontal estimates of Calderon-Zygmund type, i.e. $\begin{matrix} d T ψ \in H W_{loc}^{1, p} (Ω) & \Rightarrow T u \in L_{loc}^{p} (Ω), {| \nabla_{ℍ} ψ |}^{p} \in L_{loc}^{q} (Ω) & \Rightarrow | \nabla_{ℍ} {u |}^{p} \in L_{loc}^{q} (Ω), \end{matrix} d$ where $2 < p < 4$ , $q > 1$ .

Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity

E. Casas, O. Kavian, J.-P. Puel (1998)

ESAIM: Control, Optimisation and Calculus of Variations

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The Neumann problem for some degenerate elliptic equations

Albo Carlos Cavalheiro (2006)

Applications of Mathematics

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In the paper we study the equation $L u = f$ , where $L$ is a degenerate elliptic operator, with Neumann boundary condition in a bounded open set $Ω$ . We prove existence and uniqueness of solutions in the space $H (Ω)$ for the Neumann problem.