The talk Globally Lipschitz minimizers for variational problems with linear growth, by Erika Maringová will be held on Monday November 14, 2016 at 9:00 in room K3.
The classical example of a variational problem with linear growth is the minimal surface problem. It is well known that for smooth data such problem posses a regular (up to the boundary) solution if the domain is convex (or has positive mean
curvature). On the other hand, for non-convex domains we know that there always exist data for which the solution does exist only in the space BV (the desired trace is not attained). In the work we sharply identify the class of functionals (such that the
minimal surface problem is equivalently described by a particular functional from this class) for which we always have regular (up to the boundary) solution in any dimension for arbitrary C 1,1 domain. Furthermore, we show that the class is sharp, i.e., whenever the functional does not belong to the class then we can find data for which the solution does not exist.