POINTWISE ESTIMATES FOR POLYHARMONIC GREEN’S FUNCTION

Abstract

This thesis focuses on the polyharmonic Green’s function, one of fundamental concepts in mathematical analysis and partial differential equations. The Green’s function plays a crucial role in solving problems related to the behavior of harmonic functions, and has a wide range of applications in physics and engineering. The introduction section starts with an overview of the notation used throughout the thesis. A brief historical and literature review follows to provide context and a better understanding of the importance of the topic. The preliminary section then lays out the necessary background knowledge required for further proofs of the main theorems. The thesis then proceeds into a detailed discussion of known pointwise estimates proofs, which are crucial to understanding the Green’s function’s behavior. The main contribution of this thesis is a partial solution to an open problem from Mazya’s list of ”Seventy Five (thousand) unsolved problems in analysis and partial differential equations” from