Mapping properties of weakly singular periodic volume potentials in Roumieu classes

M. Dalla Riva, M. Lanza de Cristoforis, P. Musolino

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Abstract

The analysis of the dependence of integral operators on perturbations plays an important role in the study of inverse problems and of perturbed boundary value problems. In this paper, we focus on the mapping properties of the volume potentials with weakly singular periodic kernels. Our main result is to prove that the map which takes a density function and a periodic kernel to a (suitable restriction of the) volume potential is bilinear and continuous with values in a Roumieu class of analytic functions. This result extends to the periodic case of some previous results obtained by the authors for nonperiodic potentials, and it is motivated by the study of perturbation problems for the solutions of boundary value problems for elliptic differential equations in periodic domains.

Original languageEnglish
Pages (from-to)129-149
Number of pages21
JournalJournal of Integral Equations and Applications
Volume32
Issue number2
DOIs
Publication statusPublished - 28 Aug 2020

Keywords

  • Integral operators
  • Periodic kernels
  • Periodic volume potentials
  • Roumieu classes
  • Special nonlinear operators

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