Fully Nonlinear Elliptic Equations

Know about the book -

Fully Nonlinear Elliptic Equations is written by Luis A. Caffarelli and published by American Mathematical Soc.. It's available with International Standard Book Number or ISBN identification 0821804375 (ISBN 10) and 9780821804377 (ISBN 13).

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 equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equations, the Alexandroff estimate and Krylov-Safonov Harnack-type inequality for viscosity solutions, uniqueness theory for viscosity solutions, Evans and Krylov regularity theory for convex fully nonlinear equations, and regularity theory for fully nonlinear equations with variable coefficients.