Kral J. Integral Operators in Potential Theory

Berlin; Heidelberg; New York: Springer, 1980. — 175 p.The method of potential theory for solving boundary value problems of the Laplace equation leads to the investigation of integral equations. This method requires relatively strong smoothness restrictions on the boundary of the considered domain. For a long time there was the opinion that it is not possible to weaken these smoothness restrictions essentially. About twenty years ago there appeared some papers of the author who showed that for the investigation of limits of potentials it is not necessary to make such a priori restrictions. Since that time the author and his collaborators have developed a useful potential-theoretic method for solving boundary value problems without any smoothness assumptions on the boundary. The lecture note under review contains the main results of this theory.Introductory remark
Weak normal derivatives of potentials
Double layer potentials
Contractivity of Neumann's operator
Fredholm radius of the Neumann operator
Boundary value problems
Comments and references
Symbol index
Subject index