The talk Minimizers to varitational integrals with linear growth, by Miroslav Bulíček, will be held on Monday November 24, 2014 at 8:30 in room K4. After that, Jaroslav Hron will make a brief review about the conference "Simulation and Optimization of Extreme Fluids" held in Heidelberg University on November 10-12, 2014 (a copy of the presentation can be downloaded here)
Abstract of the talk
In the calculus of variations, a very difficult task is to minimize functionals that involve only linear growth and therefore provides only L^1 coercivity. Such problem is in general unsolvable and in fact lead to minimization problems in the space of the Radon measures. Such problem can be in nowdays solved by using the weak-lower semicontinuity of the convex functionals and one obtains a solution - a Radon measure. However, it is a natural question whether such a generalized notion is really neccesary. We show that for a very general class of functionals (having assympotically the Uhlenbeck structure), the minima is attained in the space L^1 and that no measure theory is in fact needed. Moreover, we show the relevance of such problems to the continuum mechanics setting.