Maximum principles are bedrock results in the theory of second order elliptic equations. This principle, simple enough in essence, lends itself to a quite remarkable number of subtle uses when combined appropriately with other notions. Intended for a wide audience, the book provides a clear and comprehensive explanation of the various maximum principles available in elliptic theory, from their beginning for linear equations to recent work on nonlinear and singular equations.

This volume collects papers dedicated toWalterNoll on his sixtieth birthday, January 7, 1985. They first appeared in Volumes 86-97 (1984-1987) of the Archive for Rational Mechanics and Analysis. At the request ofthe Editors the list of authors to be invited was drawn up by B.D. Coleman, M. Feinberg, and J. Serrin. WalterNoll's influence upon research into the foundations of mechanics and thermodynamics is plain, everywhere acknowledged. Less obvious is the wide effect his writings have exerted upon those who apply mechanics to special problems, but it is witnessed by the now frequent use of...

The material included in this book was first presented in a series of lectures de livered at the University of Minnesota in June 1983 in connection with the con ference "Thermodynamics and Phase Transitions." This conference was one of the principal events in the first year of operation of the Institute for Mathematics and its Applications (lMA) at the University of Minnesota. The Institute was founded under the auspices of the National Science Foun dation of the United States and the University of Minnesota and is devoted to strengthening and fostering the relation of mathematics with its...

In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = D.u + f(u). Here D. denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x O, T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of...

In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = U + f(u). Here denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x O, T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of equilibrium...