11:00-12:00 Tuesday, 1 April 2025 Auditorium, Rectorate
Abstract
Consider an integrable function $u$ defined on a open domain that satisfies some differential constraint $A u=0$, for instance curl-or divergence-free functions. In this talk, we study two related questions: First, can we find an extension of the function that is integrable on the full space and still obeys the differential constraint? Second, can we modify the function on a set of small measure such that it is not only integrable, but also bounded; again while preserving the differential constraint?We give some partial answers to both questions as well as applications to regularity theory of variational problems. Parts of this talk are based on joint work with Franz Gmeineder (U Konstanz) and Linus Behn (U Bielefeld).