Interpolation inequality
In her research, Mishra studied how interpolation inequalities are related to Sobolev extension domains. This is an interesting problem, since it leads to Keller-Lieb-Thirring inequality as an application in mathematical physics.
Homogeneous and non-homogeneous Sobolev extension domains
The results of this thesis illustrate the connection between Sobolev extension domains and homogeneous Sobolev extension domains, as well as explain why it is more difficult to control the gradient norm of an extension than to control its Lebesgue norm. The relation between Sobolev extension domains and a Brezis-Bourgain-Mironescu (BBM) inequality is also explained. Furthermore, Mishra also studied how the geometry of a domain plays an important role in extending Sobolev functions defined on it.
M.Sc. Riddhi Mishra defends her doctoral dissertation “Sobolev extension domains” on September 11th, 2026 at Agora Auditorium 3, Ag B105.
Opponent is Associate Professor Riikka Korte (Aalto University) and custos is Professor Pekka Koskela (University of Jyväskylä). The language of the dissertation is English.
