Partial Differential Equations

The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.

Inhalt

Co-area, liquid crystals, and minimal surfaces.- Nonelliptic problems and complex analysis.- Smoothness of shock front solutions for systems of conservation laws.- On degenerate monge-ampere equations in convex domains.- Initial and boundary problems for the degenerate or singular system of the filtration type.- On interior regularity of solutions of a class of hypoelliptic equations.- A counterexample to the Yamabe problem for complete noncompact manifolds.- Free boundary problems for degenerate parabolic equations.- Global perturbation of the riemann problem for the system of one-dimensional isentropic flow.- Analysis of C?-singularities for a class of operators with varying multiple characteristics.- An inverse problem for nonlocal elliptic bvp and resistivity identification.- Local ellipticity of F and regularity of F minimizing currents.- A geometric proof of the mumford compactness theorem.- Harnack inequalities for functions in De Giorgi parabolic class.- Equivariant morse theory for isolated critical orbits and its applications to nonlinear problems.- A class diffractive boundary value problem with multiple characteristic.- Existence, uniqueness and regularity of the minimizer of a certain functional.- Everywhere regularity for solutions to quasilinear elliptic systems of triangular form.- On the dirichlet problem for a class of quasilinear elliptic systems of partial differential equations in divergence form.- Initial value problems for a nonlinear singular integral-differential equation of deep water.