Interrelationships among Mechanics Numerical Analysis, Compensated Compactness, and Oscillation Theory

This paper is the written version of my lecture delivered at the Institute for Mathematics and its Applications workshop on Oscillation Theory, Computation, and Methods of Compensated Compactness. As both the titles of the workshop and this paper suggest, I believe there is a continuum of ideas and methods relating these topics. Perhaps the unifying word is “regularization” for it is a goal of applied mathematics to understand the analytical and physical meanings of the various regularizations of the conservation laws of continuum mechanics. In particular the ability to pass to the limit as the regularization parameters vanish has been a long standing problem and it seems that major progress has been made on this question recently (indeed by several of the participants of this I.M.A. workshop).