POINTWISE ESTIMATES FOR POLYHARMONIC GREEN’S FUNCTION
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Date
2023
Authors
Myrzabayeva, Galiya
Journal Title
Journal ISSN
Volume Title
Publisher
School of Sciences and Humanities
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
Description
Keywords
Type of access: Open Access, Pointwise Estimates, Polyharmonic Green’s Function
Citation
Myrzabayeva, G. (2023). Pointwise Estimates for Polyharmonic Green’s Function. School of Sciences and Humanities