Geometric Analysis and Nonlinear Partial Differential Equations

Abstract

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.