Maxwell’s Equations. Antenna Problems

  • Georges Duvaut
  • Jacques Louis Lions
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 219)


The phenomena of electromagnetism can lead to variational inequalities, either with Maxwell’s equations in a polarizable medium or, when the phenomena are coupled, with the mechanics of Bingham fluids yielding the magnetodynamics of Bingham fluids. This second possibility is treated in Duvaut-Lions [7]. The present chapter is devoted to unilateral problems connected with Maxwell’s equations. Since we cannot refer to a unified exposition of the classical phenomena of electromagnetism, we will set up equations for the phenomena in Section 2 and develop a mathematical theory for the classical solutions in Sections 4–6. This theory is indispensable for the subsequent treatment of Maxwell’s equations in a polarizable medium. Section 3 is a presentation of the physical problems under consideration.


Scalar Product Variational Inequality Electric Charge Strong Solution Polarizable Medium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • Georges Duvaut
    • 1
  • Jacques Louis Lions
    • 2
  1. 1.Mécanique ThéoretiqueUniversité de Paris VIParisFrance
  2. 2.Collège de FranceParisFrance

Personalised recommendations