Geometric Analysis and Nonlinear Partial Differential Equations

This reference features papers from the Special Session of the American Mathematical Society Meeting held in 1990 at the University of North Texas, Denton - discussing and developing research on boundary value problems for nonlinear partial differential equations and related problems.;Written by more than 15 authorities in the field, Geometric Analysis and Nonlinear Partial Differential Equations: presents methods and results of the convex bodies and geometric inequalities theory and its applications to differential equations, geometry, and mathematical physics; details recent studies on Monge-Ampere equations, emphasizing geometric inequalities governing a priori estimates of solutions and existence theorems of the Dirichlet problem for convex generalized solutions and showing the proofs of all theorems; examines the generalization of the isoperimetric inequality for two-dimensional general convex surfaces whose integral Gaussian curvature is less than 2 pi; and contains open problems on the theory of surfaces with constant mean curvature.;Geometric Analysis and Nonlinear Partial Differential Equations is for mathematical analysts, geometers, pure and applied mathematicians, physicists, engineers, computer scientists, and upper-level undergraduate and graduate students in these disciplines.

Table of Contents:
Part 1 Geometric methods in nonlinear elliptic partial differential equations and applied problems: geometric inequalities and estimates of solutions for nonlinear Euler-Lagrange equations and applied problems, Ilya J. Bakelman and William L. Perry; qualitative behaviour of solutions to a system of partial differential equations from nonlinear elasticity, Patricia Bauman; asymptotic approximations to the fundamental solutions of differential equations on manifolds, S.A. Fulling; harmonic maps with nontrivial higher-dimensional singularities, Guojun Liao and Nathan Smale; elliptic systems for a medium with microstructure, R.E. Showalter and N.J. Walkington; asymptotic behaviour of positive decreasing solutions of y=F(t,y,y'), Steven D. Taliaferro; uniqueness of capillary surfaces in wedges and cones, Thomas I. Vogel; a Neumann evolution problem for plastic antiplanar shear, Xiaodong Zhou. Part 2 Convex bodies and related topics: axiomatic convex potential theory, E.M.J. Bertin; area-reducing flows, Xiaoxi Cheng; double normals characterize bodies of constant width in Riemannian manifolds, Boris V. Dekster; quasi-time functions in Lorentzian geometry, Paul E. Ehrlich and Gerard G. Emch; the Weyl problem for surfaces in nonnegative curvature, Joseph A. Iaia; singularities and the conformal scalar curvature equation, Robert C. McOwen. Part 3 Surveys devoted to geometric inequalities and convex bodies: geometric inequalities and existence theorems for convex generalized solutions of n-dimensional Monge-Ampere equations, Ilya J. Bakelman; the isoperimetric problem for two-dimensional convex surfaces, Ilya J. Bakelman and Steven D. Taliaferro. Part 4 Problems: open problems in the geometry of equilibrium configurations, Robert Gulliver and Henry Wente.