Convex Analysis and Nonlinear Geometric Elliptic Equations

I. Bakelman was an expert in the study of nonlinear elliptic partial differential equations by methods of differential and convex geometry. In Russia he is also recognized as a reformer of mathematical education at both school and university levels. This book represents much of Bakelman's work of the last ten years (until his death in 1992). Much of his work was devoted to boundary value problems for mean curvature and Monge-Ampere equations in more than two variables and their generalizations. The book is suitable as a text book and reference work for graduate students and scientists (mathematicians but also physicists) working in the areas of convex functions and bodies, global geometric problems and nonlinear elliptic boundary value problems.

Inhalt
I. Elements of Convex Analysis.- 1. Convex Bodies and Hypersurfaces.- 2. Mixed Volumes. Minkowski Problem. Selected Global Problems in Geometric Partial Differential Equations.- II. Geometric Theory of Elliptic Solutions of Monge-Ampere Equations.- 3. Generalized Solutions of N-Dimensional Monge-Ampere Equations.- 4. Variational Problems and Generalized Elliptic Solutions of Monge-Ampere Equations.- 5. Non-Compact Problems for Elliptic Solutions of Monge-Ampere Equations.- 6. Smooth Elliptic Solutions of Monge-Ampere Equations.- III. Geometric Methods in Elliptic Equations of Second Order. Applications to Calculus of Variations, Differential Geometry and Applied Mathematics..- 7. Geometric Concepts and Methods in Nonlinear Elliptic Euler-Lagrange Equations.- 8. The Geometric Maximum Principle for General Non-Divergent Quasilinear Elliptic Equations.