Representations and estimates for inverse operators in the harmonic potential theory for polyhedra

Abstract

The paper mainly concerns the results by N. Grachev and the author in the harmonic potential theory for polyhedra. Pointwise estimates for kernels of inverse operators are presented which imply the invertibility of the integral operator generated by the double layer potential in the space of continuous functions and in $L_p$. Auxiliary pointwise estimates for Green’s kernel of the Neumann problem are proved.