Smoothness properties of Green's functions

Date
2014
Advisor
Goncharov, Alexander
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Publisher
Bilkent University
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Language
English
Type
Thesis
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Abstract

Basic notions of potential theory are explained with illustrative examples. Many important properties, including the characteristic ones, of Green’s functions that are defined by the help of equilibrium measures are given. It is discussed that for what kind of sets they are continuous. Then, it is analyzed how good their continuity can be, how smooth they can be. Examples are given for the optimal smoothness. Besides, many other examples with diverse moduli of continuity are considered. Recent developments and articles in this field are introduced in details. Finally, an open problem about finding a Cantor type set K(γ) for preassigned smoothness of Green’s function is presented.

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Keywords
Green’s functions, Smoothness
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Published Version (Please cite this version)