- Title Information
- Title
- Sobolev Estimates for Fractional Partial Differential Equations
- Type of Resource (primo)
- dissertations
- Name:
Personal
- Name Part
- Liu, Yanze
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Dong, Hongjie
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Holmer, Justin
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Pausader, Benoît
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Department of Mathematics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2023
- Physical Description
- Extent
- , None p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2023
- Genre (aat)
- theses
- 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.
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00893484")
- Topic
- Differential equations, Partial
- Subject
- Topic
- Fractional Partial Differential Equations
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20230602