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

  • Abdulrahman Alharbi

Student thesis: Master's Thesis

Abstract

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.
Date of AwardMay 30 2019
Original languageEnglish (US)
Awarding Institution
  • Computer, Electrical and Mathematical Science and Engineering
SupervisorDiogo Gomes (Supervisor)

Keywords

  • Green's Functions
  • non-divergence form
  • Fabes-Stroock
  • ABP Estimate
  • Muckenhoupt Weights

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