Degenerate Diffusions

1. Front Matter

   Pages i-xv

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2. Nonlinear, Nonlocal Problems of Fluid-Solid Interactions

   • Stuart S. Antman, Massimo Lanza De Cristoforis

   Pages 1-18

3. Curvature Dependent Phase Boundary Motion and Parabolic Double Obstacle Problems

   • J. F. Blowey, C. M. Elliott

   Pages 19-60

4. On the Harnack Inequality for Non-Negative Solutions of Singular Parabolic Equations

   • Ya-Zhe Chen, E. Dibenedetto

   Pages 61-69

5. A BMO Bound for Eigenfunctions on Riemannian Manifolds

   • Rui-Tao Dong

   Pages 71-76

6. On Some Monotonicity in Time Properties for a Quasilinear Parabolic Equation with Source

   • Victor A. Galaktionov, Sergey A. Posashkov

   Pages 77-93

7. On the asymptotic Properties of leray’s Solutions to the Exterior Steady Three-Dimensional Navier-Stokes Equations with Zero Velocity at Infinity

   • Giovanni P. Galdi

   Pages 95-103

8. Some Results on Blow up for Semilinear Parabolic Problems

   • M. A. Herrero, J. J. L. Velázquez

   Pages 105-125

9. Long-Time Behaviour of Solutions of Quasilinear Parabolic Equations

   • Kevin McLeod

   Pages 127-130

10. Spike-Layers in Semilinear Elliptic Singular Perturbation Problems†

    • Wei-Ming Ni, Izumi Takagi

    Pages 131-139

11. Evolution of Nonparametric Surfaces with Speed Depending on Curvature, III. Some Remarks on Mean Curvature and Anisotropic flows

    • Vladimir I. Oliker, Nina N. Uraltseva

    Pages 141-156

12. Continuation and Limit Behavior for Damped Quasi-Variational Systems

    • Patrizia Pucci, James Serrin

    Pages 157-173

13. Multibump Solutions of a Semilinear Elliptic PDE on Rn

    • Paul H. Rabinowitz

    Pages 175-185

14. Einstein/Yang-Mills Equations

    • J. Smoller, A. Wasserman

    Pages 187-196

15. The Dirichlet Problem for Functions of Least Gradient

    • Peter Sternberg, William P. Ziemer

    Pages 197-214

16. Asymptotic behaviour of nonlinear Parabolic Equations. Anomalous Exponents

    • Juan Luis Vazquez

    Pages 215-228

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.

• bounded mean oscillation
• differential equation
• manifold
• partial differential equation

• School of Mathematics, University of Minnesota, Minneapolis, USA

  Wei-Ming Ni

• University of Leiden, Leiden, The Netherlands

  L. A. Peletier

• Division de Matemáticas, Universidad Autonomade Madrid, Madrid, Spain

  J. L. Vazquez

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