Events

27. March 2025, 15:00 until 17:00

AKOR: About Sobolev extension domains

Seminar

Miguel García Bravo, University Completense of Madrid (Spain).

 

Abstract: Given a domain \Omega of R^n, we say that \Omega is a W^{1,p}-extension domain if there exists a constant C>0 so that for every Sobolev function f in W^{1,p}(\Omega) there exists F in W^{1,p}( R^n) so that $F|_\Omega=f$ and $||F||_{W^{1,p}( R^n)}\leq C\|f\|_{W^{1,p}(\Omega)}$. The question whether a domain has or does not have the Sobolev extension property has been widely studied during the last sixty years. In general the extension is possible whenever the domain has nice geometric properties, like having a Lipschitz boundary or being uniform (these results are due to Calderón, Stein and Jones).

 

This talk has two main objectives. First we will give a brief introduction to the history of this problem through some specific examples, exploring both necessary and sufficient geometric conditions that Sobolev extension domains must satisfy. Second, we intend to show some recent new results in the area, which are a joint work with Tapio Rajala and Jyrki Takanen. Specifically, these results try to give a better understanding of "how big" (in the sense of measure) the boundaries of Sobolev extension domains can be. We will inspect this issue through different approaches.

Calendar entry

Event location

Sem. R. DB gelb 04
1040 Wien
Wiedner Hauptstraße 8 E105-4

 

Organiser

VADOR
vador@tuwien.ac.at

 

Public

No

 

Entrance fee

No

 

Registration required

No