This book demonstrates the development of the regularity theory of solutions of fully nonlinear elliptic equations. Caffarelli and Cabr 'e offer a detailed presentation of all techniques needed to extend the classic Schauder and Calder 'on-Zygmund regularity theory for linear elliptic equations to a fully nonlinear context. The authors present key ideas and prove all results needed for the theory of viscosity solutions of nonlinear equations, and regularity theory for convex fully nonlinear equations and for fully nonlinear equations with variable coefficients. This book is suitable as a text...

Features lattice theory and portrays its structure and indicates some of its most interesting applications.

Presents a comprehensive study of the algebraic theory of quadratic forms, from classical theory to the developments, including results and proofs. Written from the viewpoint of algebraic geometry, this book includes the theory of quadratic forms over fiel

Part of "Colloquium Series", this book presents systematic treatment of orthogonal polynomials.

This volume presents a systematic and unified study of geometric nonlinear functional analysis. This area has its classical roots in the beginning of the 20th century and is a very active research area, having close connections to geometric measure theory, probability, classical analysis, combinatorics, and Banach space theory. The main theme of the book is the study of uniformly continuous and Lipschitz functions between Banach spaces (for example, differentiability, stability, approximation, existence of extensions and fixed points). This study leads naturally also to the classification of...

This monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. It provides the algebra-theoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields.

One of the major problems in the study of evolution equations of mathematical physics is the investigation of the behaviour of the solutions to these equations when time is large or tends to infinity. The related important questions concern the stability of solutions or the character of the instability if a solution is unstable. In the last few decades in the 20th century, considerable progress in this area has been achieved in the study of autonomous evolution partial differential equations. For a number of basic evolution equations of mathematical physics, it was shown that the long time...