The Mathematical Theory of Time-Harmonic Maxwell's Equations

Expansion-, Integral-, and Variational Methods

  • Andreas Kirsch
  • Frank Hettlich

Part of the Applied Mathematical Sciences book series (AMS, volume 190)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Andreas Kirsch, Frank Hettlich
    Pages 1-20
  3. Andreas Kirsch, Frank Hettlich
    Pages 21-94
  4. Andreas Kirsch, Frank Hettlich
    Pages 95-163
  5. Andreas Kirsch, Frank Hettlich
    Pages 165-225
  6. Andreas Kirsch, Frank Hettlich
    Pages 227-311
  7. Back Matter
    Pages 313-337

About this book


This book gives a concise introduction to the basic techniques needed for the theoretical analysis of the Maxwell Equations, and filters in an elegant way the essential parts, e.g., concerning the various function spaces needed to rigorously investigate the boundary integral equations and variational equations. The book arose from lectures taught by the authors over many years and can be helpful in designing graduate courses for mathematically orientated students on electromagnetic wave propagation problems. The students should have some knowledge on vector analysis (curves, surfaces, divergence theorem) and functional analysis (normed spaces, Hilbert spaces, linear and bounded operators, dual space).

Written in an accessible manner, topics are first approached with simpler scale Helmholtz Equations before turning to Maxwell Equations. There are examples and exercises throughout the book. It will be useful for graduate students and researchers in applied mathematics and engineers working in the theoretical approach to electromagnetic wave propagation.


Electromagnetic Theory Helmholtz Equations Lipschitz Domains Maxwell Equation Partial Differential Equations Sobolev Spaces

Authors and affiliations

  • Andreas Kirsch
    • 1
  • Frank Hettlich
    • 2
  1. 1.Karlsruhe Institute of Technology (KIT) Department of MathematicsKarlsruheGermany
  2. 2.Department of MathematicsKarlsruhe Institute of Technology (KIT)karlsruheGermany

Bibliographic information