OnViscosity Solutions of Fully Nonlinear Equations withMeasurable Ingredients
نویسندگان
چکیده
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 strong solutions are viscosity solutions and that viscosity solutions are twice diierentiable a.e. and the pointwise derivatives satisfy the equation a.e. An important consequence of our approach is the possibility of passage to various kinds of limits in fully nonlinear equations, extending results of this type due to Evans and Krylov. This work is to some extent expository and the main purpose of our paper is to provide an easily accessible set of tools and techniques for studying equations with measurable ingredients.
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