Approximation in the calculus of variations

Typical techniques of proving regularity of minimizers to variational functionals are based on a construction of a sequence of nice solutions to auxiliary problems, that is convergent in a relevant way. If the growth of the functional is not controlled, it is possible that such a sequence does not exist. In order to make the regularity methods work the infima of the considered functional over regular functions (e.g. smooth) and over all functions for which the functional is finite have to coincide. I will explain how a relevant density of regular functions can be ensured, when it is impossible, and what are the consequences of these phenomena.

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Mind the change of the room and the hour of the meeting!