Directions in Partial Differential Equations : Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 28—30, 1985

Directions in Partial Differential Equations covers the proceedings of the 1985 Symposium by the same title, conducted by the Mathematics Research Center, held at the University of Wisconsin, Madison. This book is composed of 13 chapters and begins with reviews of the calculus of variations and differential geometry. The subsequent chapters deal with the study of development of singularities, regularity theory, hydrodynamics, mathematical physics, asymptotic behavior, and critical point theory. Other chapters discuss the use of probabilistic methods, the modern theory of Hamilton-Jacobi equations, the interaction between theory and numerical methods for partial differential equations. The remaining chapters explore attempts to understand oscillatory phenomena in solutions of nonlinear equations. This book will be of great value to mathematicians and engineers. Content: Front Matter, Page iii Copyright, Page iv Dedication, Page v Preface, Page ix Symposium Speakers, Page xi Contributors, Pages xiii-xiv Singular Minimizers and their Significance in Elasticity, Pages 1-16, J.M. Ball Nonlinear Elliptic Equations Involving the Critical Sobolev Exponent—Survey and Perspectives, Pages 17-36, Haï Brezis The Differentiability of the Free Boundary for the n-Dimensional Porous Media Equation, Pages 37-42, Luis A. Caffarelli Oscillations and Concentrations in Solutions to the Equations of Mechanics, Pages 43-53, Ronald J. DiPerna The Connection Between the Navier-Stokes Equations, Dynamical Systems, and Turbulence Theory, Pages 55-73, Ciprian Foias, Roger Témam Blow-Up of Solutions of Nonlinear Evolution Equations, Pages 75-88, Avner Friedman Coherence and Chaos in the Kuramoto-Velarde Equation, Pages 89-111, James M. Hyman, Basil Nicolaenko Einstein Geometry and Hyperbolic Equations, Pages 113-143, S. Klainerman Recent Progress on First Order Hamilton-Jacobi Equations, Pages 145-158, P.L. Lions The Focusing Singularity of the Nonlinear Schrödinger Equation, Pages 159-201, B. LeMesurier, G. Papanicolaou, C. Sulem, P.L. Sulem A Probabilistic Approach to Finding Estimates for the Heat Kernel Associated with a Hörmander Form Operator, Pages 203-210, Daniel W. Stroock Discontinuities and Oscillations, Pages 211-233, Luc C. Tartar The Structure of Manifolds with Positive Scalar Curvature, Pages 235-242, Richard Schoen, Shing-Tung Yau Index, Pages 243-244