# Bellman equation

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The Bellman equation is the equality $\sup_{a \in \mathcal{A}} \, L_a u(x) = f(x),$ where $L_a$ is some family of linear integro-differential operators indexed by an arbitrary set $\mathcal{A}$.
The equation is uniformly elliptic with respect to any class $\mathcal{L}$ that contains all the operators $L_a$.