VADOR Events Calendar

We frequently host one off lectures on topics relating to variational analysis, dynamics and operations research.  In term-time, we host different speakers at our weekly AKOR seminar.  Seminars take place most Thursdays at 3pm in Sem. R. DB gelb 04.  Once a month, the AKOR seminar will be replaced by the Vienna Seminar on Optimization, opens an external URL in a new window - a joint venture with Radu Bot and Yurii Malitskyi of the University of Vienna

We organise the Viennese Conference on Optimal Control and Dynamic Games, typically every three years.  The next iteration - VC2025 - will take place in July 2025.  For further details on this conference, and its forerunners, please visit the VC2025, opens an external URL in a new window website.

Topics and speakers for all forthcoming events will be posted below.

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

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