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 [1], we identify the necessary and sufficient condition to existence of solution; in the case of superlinear growth [2], 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,

[1] L. Beck, M. Bulíček, and E. Maringová.  Globally Lipschitz minimizers for variational problems with linear growth, accepted to ESAIM: COCV in 2017.

[2] 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.