The Laplace Equation

Boundary Value Problems on Bounded and Unbounded Lipschitz Domains

  • Dagmar Medková

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Dagmar Medková
    Pages 1-76
  3. Dagmar Medková
    Pages 77-119
  4. Dagmar Medková
    Pages 121-224
  5. Dagmar Medková
    Pages 225-245
  6. Dagmar Medková
    Pages 247-385
  7. Dagmar Medková
    Pages 387-471
  8. Dagmar Medková
    Pages 473-651
  9. Back Matter
    Pages 653-660

About this book


This book is devoted to boundary value problems of the Laplace equation on bounded and unbounded Lipschitz domains. It studies the Dirichlet problem, the Neumann problem, the Robin problem, the derivative oblique problem, the transmission problem, the skip problem and mixed problems. It also examines different solutions - classical, in Sobolev spaces, in Besov spaces, in homogeneous Sobolev spaces and in the sense of non-tangential limit. It also explains relations between different solutions. 

The book has been written in a way that makes it as readable as possible for a wide mathematical audience, and includes all the fundamental definitions and propositions from other fields of mathematics.

This book is of interest to research students, as well as experts in partial differential equations and numerical analysis


Poisson Equation Dirichlet Problem Neumann Problem Robin Problem Derivative Oblique Problem Transmission Problem

Authors and affiliations

  • Dagmar Medková
    • 1
  1. 1.Institute of Mathematics of the Czech, Academy of SciencesPraha 1Czech Republic

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-74306-6
  • Online ISBN 978-3-319-74307-3
  • Buy this book on publisher's site