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

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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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Authors and Affiliations

  1. Centro de Investigação e Desenvolvimento em Matemática e Aplicações (CIDMA), Universidade de Aveiro, Campus Universitário de Santiago, 3810-193, Aveiro, Portugal

    Matteo Dalla Riva

  2. Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste 63, 35121, Padua, Italy

    Massimo Lanza de Cristoforis & Paolo Musolino

Authors
  1. Matteo Dalla Riva
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  2. Massimo Lanza de Cristoforis
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  3. Paolo Musolino
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Correspondence to Massimo Lanza de Cristoforis.

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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

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