Tetrahedralna wypukłość oraz tetrahedralna poliwypukłość w rachunku wariacyjnym

I plan to discuss geometric conditions for integrand f to define lower semicontinuous functional I_f(u).

Of our particular interest is tetrahedral convexity condition introduced by Agnieszka Kałamajska in 2003, which is the variant of maximum principle expressed on tetrahedrons, and the new condition which we call tetrahedral polyconvexity.

Those problems are strongly connected with open rank-one conjecture posed by Morrey in 1952, known in the multidimensional calculus of variations. The discussion will be based on joint work with Agnieszka Kałamajska.