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Duality Principles for Fully Nonlinear Elliptic Equations
Book chapter

Duality Principles for Fully Nonlinear Elliptic Equations

Diogo Aguiar Gomes
Trends in Partial Differential Equations of Mathematical Physics, pp.125-136
Progress in Nonlinear Differential Equations and Their Applications, Birkhäuser Basel
2005
DOI: https://doi.org/10.1007/3-7643-7317-2_10

Abstract

Control Markov Process Dual Problem Duality Principle Nonlinear Elliptic Equation Viscosity Solution
In this paper we use duality theory to associate certain measures to fully-nonlinear elliptic equations. These measures are the natural extension of the Mather measures to controlled stochastic processes and associated second-order elliptic equations. We apply these ideas to prove new a priori estimates for smooth solutions of fully nonlinear elliptic equations.

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