Direct Methods in the Calculus of Variations
The present monograph is a revised and augmented edition to Direct Methods in the Calculus of Variations  which is now out of print. The core and the structureofthepresentbookareessentiallytheoneof,althoughithasnow almostdoubleditssize. While writingthepresentvolume,itclearlyappearedto methatanewsubjecthasemergedandthatitdeservestobecalled“quasiconvex analysis”. This name, of course, refers to “convex analysis”, although the new subject is still in its infancy when compared with the classical one. Thecalculusofvariationsisanimmenseandveryactive?eld. Itistherefore, when writing a book, necessary to make a severe selection. This was already the case for  and is even more so for this new edition. Rather than sup- ?cially covering a lot of materials, I preferred to privilege only some aspects of the ?eld. Here are some main features of the book. I strongly emphasized the resemblances between convex and quasiconvex analysis as well as the “al- braic”aspectofthe ?eld, notably throughthe determinants andsingularvalues. Besides the classical results on lower semicontinuity and relaxation, an imp- tant feature of the monograph is the emphasis on the existence of minimizers for non convex problems.
Applications includedThe subject is a very active one, almost half of the book consists of new materials