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.
| Identifer | oai:union.ndltd.org:kaust.edu.sa/oai:repository.kaust.edu.sa:10754/655516 |
| Date | 30 May 2019 |
| Creators | Alharbi, Abdulrahman |
| Contributors | Gomes, Diogo A., Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, Laleg-Kirati, Taous-Meriem, Tzavaras, Athanasios |
| Source Sets | King Abdullah University of Science and Technology |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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