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We study fully nonlinear uniformly elliptic equations with measurable ingredients. Recently signiicant progress has been made in this area due to fundamental work of Caaarelli on W 2;p estimates for viscosity solutions. Here we present a uniied treatment of this theory based on an appropriate notion of viscosity solution. For instance, it is shown that(More)
We consider a two-player, zero-sum diierential game governed by an abstract nonlinear diierential equation of accretive type in an innnite dimensional space. We prove that the value function of the game is the unique viscosity solution of the corresponding Hamilton-Jacobi-Isaacs equation in the sense of Crandall-Lions 12]. We also discuss some properties of(More)
We consider nonlinear optimal control problems with state constraints and nonneg-ative cost in infinite dimensions, where the constraint is a closed set possibly with empty interior for a class of systems with a maximal monotone operator and satisfying certain stability properties of the set of trajectories that allow the value function to be lower(More)
We introduce the notion of a good" solution of a fully nonlinear uniformly elliptic equation. It is proven that good" solutions are equivalent to L p-viscosity solutions of such equations. The main contribution of the paper is an explicit construction of elliptic equations with strong solutions that approximate any given fully nonlinear uniformly elliptic(More)
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