© 2018

The Laplace Equation

Boundary Value Problems on Bounded and Unbounded Lipschitz Domains


  • Discusses boundary value problems of the Poisson equations on bounded and unbounded domains

  • Examines different solutions - classical, in Sobolev spaces, in Besov spaces, in homogeneous Sobolev spaces, and in the sense of non-tangential limits

  • Studies the Dirichlet problem, the Neumann problem, the Robin problem, the derivative oblique problem, the transmission problem, the skip problem and the obstacle problem


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

  1. 1.Institute of Mathematics of the Czech, Academy of SciencesPraha 1Czech Republic

About the authors

Doc. RNDr. Dagmar Medková (CSc) is a research fellow at the Czech Academy of Sciences' Institute of Mathematics.

Bibliographic information

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“This book gives a very nice introduction to the modern theory of partial differential equations and it collects together the most relevant results in several theories related to the regularity theory and the boundary value problems on bounded and unbounded domains. The material is also accessible for experts in other fields and for doctoral students. Detailed arguments are given to several results that are difficult to find in the literature.” (Juha K. Kinnunen, Mathematical Reviews, December, 2018)