Ebook: Degenerate Diffusions

This volume is the proceedings of the IMA workshop "Degenerate Diffusions" held at the University of Minnesota from May 13-May 18, 1991. The workshop consisted of two parts. The emphasis of the first four days was on current progress or new problems in nonlinear diffusions involving free boundaries or sharp interfaces. Analysts and geometers will find some of the mathematical models described in this volume interesting; and the papers of more pure mathematical nature included here should provide applied mathematicians with powerful methods and useful techniques in handling singular perturbation problems as well as free boundary problems. The last two days of the workshop were a celebration of James Serrin's 65th birthday. A wide range of topics was covered in this part of the workshop. As a consequence, the scope of this book is much broader than what the title Degenerate Diffusions might suggest.

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Content:
Front Matter....Pages i-xv
Nonlinear, Nonlocal Problems of Fluid-Solid Interactions....Pages 1-18
Curvature Dependent Phase Boundary Motion and Parabolic Double Obstacle Problems....Pages 19-60
On the Harnack Inequality for Non-Negative Solutions of Singular Parabolic Equations....Pages 61-69
A BMO Bound for Eigenfunctions on Riemannian Manifolds....Pages 71-76
On Some Monotonicity in Time Properties for a Quasilinear Parabolic Equation with Source....Pages 77-93
On the asymptotic Properties of leray’s Solutions to the Exterior Steady Three-Dimensional Navier-Stokes Equations with Zero Velocity at Infinity....Pages 95-103
Some Results on Blow up for Semilinear Parabolic Problems....Pages 105-125
Long-Time Behaviour of Solutions of Quasilinear Parabolic Equations....Pages 127-130
Spike-Layers in Semilinear Elliptic Singular Perturbation Problems?....Pages 131-139
Evolution of Nonparametric Surfaces with Speed Depending on Curvature, III. Some Remarks on Mean Curvature and Anisotropic flows....Pages 141-156
Continuation and Limit Behavior for Damped Quasi-Variational Systems....Pages 157-173
Multibump Solutions of a Semilinear Elliptic PDE on Rn ....Pages 175-185
Einstein/Yang-Mills Equations....Pages 187-196
The Dirichlet Problem for Functions of Least Gradient....Pages 197-214
Asymptotic behaviour of nonlinear Parabolic Equations. Anomalous Exponents....Pages 215-228

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Content:
Front Matter....Pages i-xv
Nonlinear, Nonlocal Problems of Fluid-Solid Interactions....Pages 1-18
Curvature Dependent Phase Boundary Motion and Parabolic Double Obstacle Problems....Pages 19-60
On the Harnack Inequality for Non-Negative Solutions of Singular Parabolic Equations....Pages 61-69
A BMO Bound for Eigenfunctions on Riemannian Manifolds....Pages 71-76
On Some Monotonicity in Time Properties for a Quasilinear Parabolic Equation with Source....Pages 77-93
On the asymptotic Properties of leray’s Solutions to the Exterior Steady Three-Dimensional Navier-Stokes Equations with Zero Velocity at Infinity....Pages 95-103
Some Results on Blow up for Semilinear Parabolic Problems....Pages 105-125
Long-Time Behaviour of Solutions of Quasilinear Parabolic Equations....Pages 127-130
Spike-Layers in Semilinear Elliptic Singular Perturbation Problems?....Pages 131-139
Evolution of Nonparametric Surfaces with Speed Depending on Curvature, III. Some Remarks on Mean Curvature and Anisotropic flows....Pages 141-156
Continuation and Limit Behavior for Damped Quasi-Variational Systems....Pages 157-173
Multibump Solutions of a Semilinear Elliptic PDE on Rn ....Pages 175-185
Einstein/Yang-Mills Equations....Pages 187-196
The Dirichlet Problem for Functions of Least Gradient....Pages 197-214
Asymptotic behaviour of nonlinear Parabolic Equations. Anomalous Exponents....Pages 215-228
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