Description
- Abstract:
- In this thesis, we study the non-local differential equations. The first part is a comprehensive study of $L_p$ estimates for time fractional wave equations of order $\alpha \in (1,2)$ in the whole space, a half space, or a cylindrical domain. We obtain weighted mixed-norm estimates and solvability of the equations in both non-divergence form and divergence form when the leading coefficients have small mean oscillation in small cylinders. In the second part, we obtain $L_p$ estimates for {fractional parabolic} equations with space-time non-local operators. We also derive a weighted mixed-norm estimate for the equations with operators that are local in time, i.e., $\alpha = 1$, which extend the previous results by using a quite different method.
- Notes:
- Thesis (Ph. D.)--Brown University, 2023
Citation
Liu, Yanze,
"Sobolev Estimates for Fractional Partial Differential Equations"
(2023).
Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://repository.library.brown.edu/studio/item/bdr:52k2tgb9/
