Analytic Dependence of Volume Potentials Corresponding to Parametric Families of Fundamental Solutions

Abstract

We show that volume potentials associated to a parameter dependent analytic family of weakly singular kernels depend real-analytically upon the density function and on the parameter. Then we consider the special case in which the analytic family corresponds to a family of fundamental solutions of second order differential operators with constant coefficients.Peer reviewe

A mapping property of the heat volume potential

“…We also note that a potential theoretic approach has recently revealed to be very effective to deal with elliptic problems in singularly perturbed domains. For this reason, mapping properties of elliptic volume potentials have been also considered in view of applications to perturbation problems (see Dalla Riva, Lanza de Cristoforis and Musolino [4,5]). More details on the potential theoretic approach to perturbation problems for elliptic equations and results on volume potentials can be found in the monograph by Dalla Riva, Lanza de Cristoforis and Musolino [6].…”