We investigate comparison and existence results for viscosity solutions of fully nonlinear,
second-order, elliptic, possibly degenerate equations. These results complement those …

These lectures present the most basic theory of" viscosity solutions" of fully nonlinear scalar
partial differential equations of first and second order. Other contributions to this volume …

The notion of viscosity solutions of scalar fully nonlinear partial differential equations of
second order provides a framework in which startling comparison and uniqueness …

This book is an introduction to optimal stochastic control for continuous time Markov
processes and the theory of viscosity solutions. It covers dynamic programming for …

A powerful and usable class of methods for numerically approximating the solutions to
optimal stochastic control problems for diffusion, reflected diffusion, or jump-diffusion models …

The goal of the book is to extend classical regularity theorems for solutions of linear elliptic
partial differential equations to the context of fully nonlinear elliptic equations. This class of …

Semiconcavity is a natural generalization of concavity that retains most of the good
properties known in convex analysis, but arises in a wider range of applications. This text is …

This paper treats degenerate parabolic equations of second order (14.1) u_t+ F (∇ u, ∇^ 2
u)= 0 related to differential geometry, where∇ stands for spatial derivatives of u= ut, x) in x∈ …

Hamilton-Jacobi equations and other types of partial differential equa tions of the first order
are dealt with in many branches of mathematics, mechanics, and physics. These equations …

In this book, we take the notion of nonlinear expectation as a fundamental notion of an
axiomatical system. This enables us to get directly many new and fundamental results: such …