Seminar on Nonlinear Partial Differential EquationsS.S. Chern When the Mathematical Sciences Research Institute was started in the Fall of 1982, one of the programs was "non-linear partial differential equations". A seminar was organized whose audience consisted of graduate students of the University and mature mathematicians who are not experts in the field. This volume contains 18 of these lectures. An effort is made to have an adequate Bibliography for further information. The Editor wishes to take this opportunity to thank all the speakers and the authors of the articles presented in this volume for their cooperation. S. S. Chern, Editor Table of Contents Geometrical and Analytical Questions Stuart S. Antman 1 in Nonlinear Elasticity An Introduction to Euler's Equations Alexandre J. Chorin 31 for an Incompressible Fluid Linearizing Flows and a Cohomology Phillip Griffiths 37 Interpretation of Lax Equations The Ricci Curvature Equation Richard Hamilton 47 A Walk Through Partial Differential Fritz John 73 Equations Remarks on Zero Viscosity Limit for Tosio Kato 85 Nonstationary Navier-Stokes Flows with Boundary Free Boundary Problems in Mechanics Joseph B. Keller 99 The Method of Partial Regularity as Robert V. |
Contents
| 1 | |
An Introduction to Eulers Equations Alexandre J Chorin | 31 |
The Ricci Curvature Equation Richard Hamilton | 47 |
A Walk Through Partial Differential Fritz John | 73 |
Free Boundary Problems in Mechanics Joseph B Keller | 99 |
The Method of Partial Regularity as Robert V Kohn | 117 |
Stress and Riemannian Metrics in Jerrold E Marsden | 173 |
Analytical Theories of Vortex Motion John Neu | 203 |
The Minimal Surface Equation R Osserman | 237 |
A Survey of Removable Singularities John C Polking | 261 |
Applications of the Maximum Principle M H Protter | 293 |
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Common terms and phrases
Antman argument assume ball Bernstein's Theorem bounded codimension coefficients compact support constant convergence convex convex function critical points curve d-closed defined deformation denote derivatives differential inequality dimension Dirichlet domain DRc(g dxdt elliptic energy entire solution entropy estimates existence finite flow fluid follows formula geometry given grad gradient Hamiltonian harmonic map Hence hypersurfaces implies inequality initial data integral Lemma linear manifold Marsden Math mathematical maximum principle Mech mechanics membrane metric g minimal surface minimal surface equation Navier-Stokes equations neighborhood nonlinear elasticity nonpositive norm partial differential equations plane plasma Poisson bracket positive proof prove Rc(g regularity removable singularities result Ricci curvature Riemannian satisfies smooth space submanifold Suppose tends to zero tensor theory unique variables variation vector velocity viscosity vortex vorticity weak solution дх