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On the Lp-Integrability of Green’s function for Elliptic Operators

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.

Identiferoai:union.ndltd.org:kaust.edu.sa/oai:repository.kaust.edu.sa:10754/655516
Date30 May 2019
CreatorsAlharbi, Abdulrahman
ContributorsGomes, Diogo A., Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, Laleg-Kirati, Taous-Meriem, Tzavaras, Athanasios
Source SetsKing Abdullah University of Science and Technology
LanguageEnglish
Detected LanguageEnglish
TypeThesis

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