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.
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Dalla Riva, M., Lanza de Cristoforis, M. & Musolino, P. Analytic Dependence of Volume Potentials Corresponding to Parametric Families of Fundamental Solutions. Integr. Equ. Oper. Theory 82, 371–393 (2015). https://doi.org/10.1007/s00020-015-2236-3
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DOI: https://doi.org/10.1007/s00020-015-2236-3