On the trace of Sobolev spaces on the Von Koch’s snowflake – Michal Wojciechowski (Mathematical Institute of the Polish Academy of Science)


Sala Seminari (Dip. Matematica).


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.

Torna in cima