Summer 2020 Mapping properties of weakly singular periodic volume potentials in Roumieu classes
M. Dalla Riva, M. Lanza de Cristoforis, P. Musolino
J. Integral Equations Applications 32(2): 129-149 (Summer 2020). DOI: 10.1216/jie.2020.32.129


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.


Download Citation

M. Dalla Riva. M. Lanza de Cristoforis. P. Musolino. "Mapping properties of weakly singular periodic volume potentials in Roumieu classes." J. Integral Equations Applications 32 (2) 129 - 149, Summer 2020.


Received: 12 January 2018; Revised: 10 June 2018; Accepted: 12 June 2019; Published: Summer 2020
First available in Project Euclid: 28 August 2020

zbMATH: 07282580
MathSciNet: MR4141401
Digital Object Identifier: 10.1216/jie.2020.32.129

Primary: 31B10 , 47H30

Keywords: Integral‎ ‎Operators , periodic kernels , periodic volume potentials , Roumieu classes , special nonlinear operators

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium


This article is only available to subscribers.
It is not available for individual sale.

Vol.32 • No. 2 • Summer 2020
Back to Top