Resolvent Estimates in (weighted) Lp spaces for the Stokes Operator in Lipschitz Domains

Resolvent Estimates in (weighted) Lp spaces for the Stokes Operator in Lipschitz Domains

Dikland, Tim (TU Delft Electrical Engineering, Mathematics and Computer Science)

Veraar, Mark (mentor)
Frey, Dorothee (mentor)
van Gennip, Yves (graduation committee)

Delft University of Technology

2019-10-23

Recently, by Z. Shen, resolvent estimates for the Stokes operator were established in L^p(Ω) when Ω is a Lipschitz domain in R^d, with d≥3 and |1/p-1/2|<1/(2d)+ε. This result implies that the Stokes operator generates a bounded analytic semigroup in L^p(Ω) in the case that Ω is a three-dimensional Lipschitz domain and 3/2-ε<p<3+ε. To fully understand the work of Z. Shen, a lot of background information is needed. In this thesis the resolvent estimates are studied in detail in the case d=3. In the end the results of Shen are extended to resolvent estimates in L^p(w,Ω), where Ω is a three-dimensional Lipschitz domain, |1/p-1/2|<1/6, and w∈A_2p/3∩RH_3/(3-p) is a weight function that belongs to an intersection of a Muckenhoupt weight class and satisfies a reverse Hölder inequality.

Stokes operator
Resolvent Esimtate
Lipschitz domain
reverse Hölder
Layer potential

http://resolver.tudelft.nl/uuid:6a725f7a-aa0d-47d8-ad05-3811f3050145

Student theses

master thesis

© 2019 Tim Dikland