Variational Problems: The Lavrentiev Phenomenon and Applications

本研究将致力于分析的问题，在变分法中，奇异极小可能会出现。 特别是，它们包括的问题，如标题下描述的间隙效应“拉夫连季耶夫现象”可能出现。 可以预见，在这项调查中的成功结果可能会有重要的影响，在非线性弹性材料的研究。因此，它们有可能在分析和开发“智能”材料方面提供额外的专业知识。这种材料的有效开发可能对我们目前的材料技术有相当大的帮助。

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.