This research will be devoted to the analysis of problems in the calculus of variations in which singular minimizers may arise. In particular they include problems where gap effects like those described under the heading "Lavrentiev phenomenon" can arise. It is anticipated that successful results in this investigation may have important consequences in the study of nonlinear elastic materials. Thus they have the potential of providing additional expertise in the analysis and development of "smart" materials. The effective development of such materials could be of considerable aid to our current materials technology.
