Green fonksiyonlarının pürüzsüzlük özellikleri

Basic notions of potential theory are explained with illustrative examples. Many important properties, including the characteristic ones, of Green's functions that are de ned 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 eld are introduced in details. Finally, an open problem about nding a Cantor type set K(y) for preassigned smoothness of Green's function is presented.