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A Right Inverse Operator for \({\text {curl}}+\lambda \) and Applications

  • Briceyda B. Delgado
  • Vladislav V. KravchenkoEmail author
Article
  • 16 Downloads

Abstract

A general solution of the equation \({\text {curl}}\,\vec {w}+\lambda \vec {w}=\vec {g},\,\lambda \in \mathbb {C},\,\lambda \ne 0\) is obtained for an arbitrary bounded domain \(\Omega \subset \mathbb {R}^{3}\) with a Liapunov boundary and \(\vec {g}\in W^{p,{\text {div}}}\left( \Omega \right) =\left\{ \vec {u}\in L^{p}\left( \Omega \right) :\,{\text {div}}\,\vec {u}\in L^{p}\left( \Omega \right) ,\,1<p<\infty \right\} \). The result is based on the use of classical integral operators of quaternionic analysis. Applications of the main result are considered to a Neumann boundary value problem for the equation \({\text {curl}}\,\vec {w}+\lambda \vec {w}=\vec {g}\) as well as to the nonhomogeneous time-harmonic Maxwell system for achiral and chiral media.

Keywords

Div-curl system Monogenic functions Helmholtz equation Metaharmonic conjugate function Neumann boundary value problem Maxwell equations 

Mathematics Subject Classification

30G20 30G35 35Q60 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Regional Mathematical Center of Southern Federal UniversityRostov-on-DonRussia

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