Venue
Sala Seminari (Dip. Matematica).
Abstract
We show that the boundary trace operator on Sobolev space of functions with summable gradient on von Koch’s snowflake has a right inverse. This contrasts with the case of domains with nice boundaries in which, according to Petree’s theorem, a right inverse does not exist. Our proof is based on the characterization of the trace space. As a by-product we give a very simple proof of Petree’s theorem. This is joint work with Krystian Kazaniecki.