Türkün, Can2016-01-082016-01-082014http://hdl.handle.net/11693/18339Ankara : The Department of Mathematics and the Granduate School of Engineering and Science of Bilkent University, 2014.Thesis (Master's) -- Bilkent University, 2014.Includes bibliographical references leaves 58-59.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.vii, 59 leavesEnglishinfo:eu-repo/semantics/openAccessGreen’s functionsSmoothnessQC174.17.G68 T87 2014Green functions.Smoothness of functions.ThesisB148342