Dissertation: Sobolev extension sets in metric spaces (Koivu)
In his dissertation thesis Jesse Koivu combines the concept of a Sobolev space and the extension of a function. He considers in what kind of sets Sobolev functions can be extended.
- The results of the thesis have been researched a lot in the so called Euclidean spaces, but in the metric case there is many interesting new problems and new proof methods, even if the results are very similar to the old usual results, explains Doctoral Researcher Jesse Koivu from the University of Jyväskylä.
Approximating sets
Koivu also researched how one can approximate sets with extension sets.
- This is an interesting problem, since not all sets are extension sets, but sometimes we still want to extend functions that are not defined on a set that is not an extension set, says Koivu.
Different extensions and approximating functions
There exist many different kinds of extension sets, which was a common theme in Koivu’s thesis. He studied connections of different extension sets to each other.
- My research largely considers the question “Under what assumptions is an extension set of one kind also an extension set of another kind?”. This connects naturally to the approximation problem above, since unifying two types of extension sets allows approximating sets with either type of the extension sets, clarifies Koivu.
Koivu also studied how one type of Sobolev-function can be used to approximate another type of Sobolev-functions.
- This is also a classical result in the Euclidean case and an interesting generalisation to the metric space, says Koivu.
M.Sc. Jesse Koivu defends his doctoral dissertation “On BV and Sobolev extension sets in metric measure spaces” on Friday 20th of February at 12.00 at Agora Auditorio 2 (Ag B105). Opponent is Academy Research Fellow and University Lecturer Aleksis Koski (Aalto University) and custos is Professor Tapio Rajala (University of Jyväskylä).
The thesis ”On BV and Sobolev extension sets in metric measure spaces” is available in the JYX archive at: https://jyx.jyu.fi/jyx/Record/jyx_123456789_108486
Further information:
- Doctoral Researcher Jesse Koivu, +358503685368, jesse.j.j.koivu@jyu.fi
