Some recent methods for partialdifferential equations of divergence form

Some recent methods for solving second-order nonlinearpartial differential equations of divergence form and relatednonlinear problems are surveyed. These methods include entropymethods via the theory of divergence-measure fields forhyperbolic conservation laws, kinetic methods via kineticformulations for degenerate parabolichyperbolic equations, andfree-boundary methods via free-boundary iterations formultidimensional transonic shocks for nonlinear equation ofmixed elliptic-hyperbolic type. Some recent trends in thisdirection are also discussed.Dedicated to IMPA on the occasion of its 50^th anniversary