The Dirichlet problem and its inverse in a domain with compact regular boundary for the diffusion and Coulomb potentials with corrections (Q1594159)

This survey paper considers potential theory in \(\mathbb R^3\) for a convolution kernel of the form \[ K(x)=(4\pi|x|)^{-1}\int\exp(-\gamma|x|s)\, dH(s), \] where \(H\) is a given real normalized function on the interval \([0,\infty)\) with a locally bounded variation and \(\gamma >0\). After enumeration of properties of the potential \(U_K\) the corresponding Dirichlet problem is studied.