On the properties of potentials and boundary value problems in the case of a boundary surface with a conical point

We consider the properties of the double and simple layer potentials in the case of a surface with a conical point. On the basis of these properties and a theorem on an alternative, we study the Dirichlet and Neumann boundary value problems by the method of integral equations in the case of a boundary surface with a conical point and prove the existence and uniqueness of solutions in the Hölder class and in a weighted Hölder class.