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.
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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.
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