[Turkmath:4354] Sabancı Mathematics Colloquium - Wed 4th of March

[Michel Lavrauw]

You are cordially invited to the Mathematics Colloquium on Wednesday 4 March 2020  at 13:40 in the FENS building on Sabancı Campus in room G035.

Speaker: Martin Kru\v{z}\'{\i}k
Title: Lower semicontinuity of integral functionals

Abstract: In 1830, B. Bolzano observed that continuous functions attain extreme values on compact intervals of reals. This idea was then significantly extended  around 1900 by D. Hilbert who set up a framework, called the direct method,   in which we can prove existence of minimizers/maximizers of nonlinear functionals. Semicontinuity plays a crucial role in these considerations.     
In 1965,  N.G. Meyers significantly extended   lower semicontinuity  results for integral functionals depending on maps and their  gradients   available at that time.  We recapitulate the   development on this topic from that time on. Special attention will be paid   to applications in  continuum mechanics of solids. In particular, we review  existing results applicable in nonlinear elasticity and emphasize the key importance of convexity and  subdeterminants of matrix-valued gradients.
Finally, we mention a couple of 
open problems  and  outline various generalizations of these results to more general first-order partial differential operators with applications to electromagnetism, for instance.

Kind regards,
Michel Lavrauw