Mathematical Sciences: NSF/CBMS Regional Conference in Mathematical Sciences- "Compensated Compactness, Homogenization and H-Measures" June 28-July 3,1993

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Many important physical phenomena are modelled by nonlinear partial differential equations. The aim of this conference is to present some general techniques recently developed to study existence and qualitative behaviour of solutions to nonlinear PDE's. In particular it will focus on competing effects of oscillations and nonlinearity in partial differential equations. The theory of compensated compactness was developed to solve some fundamental problems of continuum mechanics using tools of functional analysis, weak convergence and Young measures. Studying oscillations solely by means of Young measures gave a static and not a dynamic description. To further understand homogenization, geometric optics and obtain more precise results on propagation of oscillations and concentrations effects, Luc Tartar introduced a quadratic microlocal tool: the H-measures. The methods that will be discussed in this conference are aimed to answer basic questions aring in physics and applied mathematics by means of rigorous mathematical tools. This project will support an NSF/CBMS Regional Research Conference in the Mathematical Sciences on Compensated Compactness, Homogenization and H-Measures, to be held June 27 to July 1, 1993, at the University of California, Santa Cruz. This project will support an NSF-CBMS Regional Research Conference in the Mathematical Sciences on Compensated Compactness, Homogenization and H-Measures to be held June 28 - July 3, 1993, at the University of California, Santa Cruz. Professor Luc Tartar of Carnegie Mellon University and a corresponding member of the French Academy of Sciences, will be the principal lecturer. To stimulate interest and activity in mathematical research, the National Science Foundation each year supports a number of NSF-CBMS Regional Research Conferences in the Mathematical Sciences. Each five-day conference features a distinguished lecturer who delivers ten lectures on a topic on important current research in one sharply focused area of the mathematical sciences. The lecturer subsequently prepares an expository monograph based upon these lectures, which is normally published by the American Mathematical Society or the Society for Industrial and Applied Mathematics, or jointly by the American Statistical Association and the Institute of Mathematical Statistics. Certain features differentiate these conferences from typical research conferences. These are: (1) Focus on a single important and timely area of research by a leading practitioner, (2) Continued effect and local stimulation through regional emphasis, (3) Panel review for quality, breadth, and timeliness, and (4) Published monographs for a wider audience.