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

Matteo Dalla Riva; Massimo Lanza de Cristoforis; Paolo Musolino

doi:10.1007/s00020-015-2236-3

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

Matteo Dalla Riva, Massimo Lanza de Cristoforis^*, Paolo Musolino

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	371-393
Number of pages	23
Journal	Integral Equations and Operator Theory
Volume	82
Issue number	3
DOIs	https://doi.org/10.1007/s00020-015-2236-3
Publication status	Published - 12 Jul 2015

Keywords

domain perturbation
second order differential operators with constant coefficients
special nonlinear operators
Volume potentials

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title = "Analytic Dependence of Volume Potentials Corresponding to Parametric Families of Fundamental Solutions",

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.",

keywords = "domain perturbation, second order differential operators with constant coefficients, special nonlinear operators, Volume potentials",

author = "{Dalla Riva}, Matteo and {Lanza de Cristoforis}, Massimo and Paolo Musolino",

year = "2015",

month = jul,

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doi = "10.1007/s00020-015-2236-3",

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T1 - Analytic Dependence of Volume Potentials Corresponding to Parametric Families of Fundamental Solutions

AU - Dalla Riva, Matteo

AU - Lanza de Cristoforis, Massimo

AU - Musolino, Paolo

PY - 2015/7/12

Y1 - 2015/7/12

N2 - 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.

AB - 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.

KW - domain perturbation

KW - second order differential operators with constant coefficients

KW - special nonlinear operators

KW - Volume potentials

UR - http://www.scopus.com/inward/record.url?scp=84930762034&partnerID=8YFLogxK

U2 - 10.1007/s00020-015-2236-3

DO - 10.1007/s00020-015-2236-3

M3 - Article

AN - SCOPUS:84930762034

SN - 0378-620X

VL - 82

SP - 371

EP - 393

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 3

ER -

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

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