Partial Differential Equations

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.