On the Lp-Integrability of Green’s function for Elliptic Operators
Type
ThesisAuthors
Alharbi, Abdulrahman
Advisors
Gomes, Diogo A.
Committee members
Laleg-Kirati, Taous-Meriem
Tzavaras, Athanasios

Date
2019-05-30Permanent link to this record
http://hdl.handle.net/10754/655516
Metadata
Show full item recordAbstract
In this thesis, we discuss some of the results that were proven by Fabes and Stroock in 1984. Our main purpose is to give a self-contained presentation of the proof of this results. The first result is on the existence of a “reverse H ̈older inequality” for the Green’s function. We utilize the work of Muckenhoupt on the reverse Ho ̈lder inequality and its connection to the A∞ class to establish a comparability property for the Green’s functions. Additionally, we discuss some of the underlying preliminaries. In that, we prove the Alexandrov-Bakelman-Pucci estimate, give a treatment to the Ap and A∞ classes of Muckenhoupt, and establish two intrinsic lemmas on the behavior of Green’s function.Citation
Alharbi, A. (2019). On the Lp-Integrability of Green’s function for Elliptic Operators. KAUST Research Repository. https://doi.org/10.25781/KAUST-71531ae974a485f413a2113503eed53cd6c53
10.25781/KAUST-71531