Degenerate Diffusions

This IMA Volume in Mathematics and its Applications DEGENERATE DIFFUSIONS is based on the proceedings of a workshop which was an integral part of the 1990- 91 IMA program on "Phase Transitions and Free Boundaries". The aim of this workshop was to provide some focus in the study of degenerate diffusion equations, and by involving scientists and engineers as well as mathematicians, to keep this focus firmly linked to concrete problems. We thank Wei-Ming Ni, L.A. Peletier and J.L. Vazquez for organizing the meet­ ing. We especially thank Wei-Ming Ni for editing the proceedings. We also take this opportunity to thank those agencies whose financial support made the workshop possible: the Army Research Office, the National Science Foun­ dation, and the Office of Naval Research. A vner Friedman Willard Miller, Jr. PREFACE This volume is the proceedings of the IMA workshop "Degenerate Diffusions" held at the University of Minnesota from May 13 to May 18, 1991.

Nonlinear, nonlocal problems of fluid-solid interactions.- Curvature dependent phase boundary motion and parabolic double obstacle problems.- On the Harnack inequality for non-negative solutions of singular parabolic equations.- A BMO bound for eigenfunctions on Riemannian manifolds.- On some monotonicity in time properties for a quasilinear parabolic equation with source.- On the asymptotic properties of Leray’s solutions to the exterior steady three-dimensional Navier-Stokes equations with zero velocity at infinity.- Some results on blow up for semilinear parabolic problems.- Long-time behaviour of solutions of quasilinear parabolic equations.- Spike-layers in semilinear elliptic singular perturbation problems.- Evolution of nonparametric surfaces with speed depending on curvature, III. Some remarks on mean curvature and anisotropic flows.- Continuation and limit behavior for damped quasi-variational systems.- Multibump solutions of a semilinear elliptic PDE on Rn.- Einstein/Yang-Mills equations.- The Dirichlet problem for functions of least gradient.- Asymptotic behaviour of nonlinear parabolic equations. Anomalous exponents.