SOME PROBLEMS IN THE CALCULUS OF VARIATIONS.

                                   ARRIGO CELLINA

        Abstract.
We present some results and open problems in the Calculus of Variations.
                               
  1. Introduction
   The text that follows is a very expanded version of the Andrzej Lasota Commem-
orative Lecture, given in Katowice in January 2016. The Lecture was presented to
an audience of mathematicians, not necessarily specialists in the Calculus of Varia-
tions. This text, although it is a survey of several recent results and open problems
in the Calculus of Variations that have been of great interest to the author, has
retained the character of being addressed to non-specialists. The topics that are
presented are: the necessary conditions; the existence of solutions to problems of
slow growth and some problems concerning the regularity of solutions. Very little
or none preliminary knowledge of these topics is required.
[....]

The whole  article is under reviewing process yet and will be published
in  Annales Mathematicae Silesianae.