This IMA Volume in Mathematics and its Applications Metastability and Incompletely Posed Problems represents the proceedings of a workshop which was an integral part of the 19R4-R5 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EOIIATIONS. We are grateful to the Scientific Committee: ,I.L. Eri cksen D. Kinderlehrer H. Rrezis C. Dafermos for their dedication and hard work in developing an imaginative, stimulating, and productive year-long program. George R. Sell Hans Weinberger Preface Most equilibrium events in nature do not realize configurations of minimum energy. They are only metastable. Available knowledge of constitutive relations and environmental interactions may be limiterl. As a result, many configurations may he compatible with the rlata. Such questions are incompletely poserl. The papers in this volume address a wide variety of these issues as they are perceived by the material scientist and the mathematician. They represent a portion of the significant activity which has been underway in recent years, from the experimental arena and physical theory to the analysis of differential equations and computation.

Dissipative Mechanisms.- Does Rank-One Convexity Imply Quasiconvexity?.- Metastable Harmonic Maps.- Bifurcation of Constrained Problems in Thermoelasticity.- The Compressible Reynolds Lubrication Equation.- Twinning of Crystals I.- Quasiconvexity and Partial Regularity in the Calculus of Variations.- to Pattern Selection in Dendritic Solidification.- Some Results and Conjectures in the Gradient Theory of Phase Transitions.- The Stability and Metastability of Quartz.- Continuation Theorems for Schrodinger Operators.- Twinning of Crystals II.- Simulation of Pseudo-Elastic Behaviour in a System of Rubber Ballons.- Asymptotic Problems in Distributed Systems.- Stability of Nonlinear Waves.- The Nash-Moser Technique for an Inverse Problem in Potential Theory Related to Geodesy.- Variational Stability and Relaxed Dirichlet Problems.- A Contribution to the Description of Natural States for Elastic Crystalline Solids.- Nonlocal Problems in Electromagnetism.- Hyperbolic Aspects in the Theory of the Porous Medium Equation.- Green's Formulas for Linearized Problems with Live Loads.- Some Aspects of Adiabatic Shear Bands.- Information about other Volumes in this Program.