The seminar will take place on Monday, March 19, 2018 at 9:00 am in K4. Erika Maringová will give a lecture “Up to the boundary Lipschitz regularity for variational problems”.
Abstract: We prove the existence of a regular solution to a wide class of convex, variational integrals. Via technique of construction of the barriers we show that the solution is Lipschitz up to the boundary. For the linear growth case , we identify the necessary and sufficient condition to existence of solution; in the case of superlinear growth , we provide the sufficient one. The result is not restricted to any geometrical assumption on the domain, only its regularity plays the role. The talk will be based on two works,
 L. Beck, M. Bulíček, and E. Maringová. Globally Lipschitz minimizers for variational problems with linear growth, accepted to ESAIM: COCV in 2017.
 M. Bulíček, E. Maringová, B. Stroffolini and A. Verde. A boundary regularity result for minimizers of variational integrals with nonstandard growth, accepted to Nonlinear Analysis in 2018.