6533b829fe1ef96bd128af28
RESEARCH PRODUCT
Mapping properties of weakly singular periodic volume potentials in Roumieu classes
M. Lanza De CristoforisPaolo MusolinoM. Dalla Rivasubject
Integral operatorsNumerical AnalysisIntegral operators; Periodic kernels; Periodic volume potentials; Roumieu classes; Special nonlinear operatorsDifferential equationApplied Mathematics010102 general mathematicsMathematical analysisSpecial nonlinear operatorsBilinear interpolationPerturbation (astronomy)Probability density functionInverse problem01 natural sciences31B10010101 applied mathematicsSettore MAT/05 - Analisi MatematicaKernel (statistics)Boundary value problemPeriodic volume potentials0101 mathematics47H30Roumieu classesPeriodic kernelsAnalytic functionMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-06-01 |