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The Laplace Equation

Boundary Value Problems on Bounded and Unbounded Lipschitz Domains

  • Book
  • © 2018

Overview

Authors:
  1. Dagmar Medková

    1. Institute of Mathematics of the Czech, Academy of Sciences, Praha 1, Czech Republic

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  • 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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Preliminaries

    • Dagmar Medková
    Pages 1-76

  3. Harmonic Functions

    • Dagmar Medková
    Pages 77-119

  4. Solutions of the Poisson Equation

    • Dagmar Medková
    Pages 121-224

  5. PWB Solutions of the Dirichlet Problem

    • Dagmar Medková
    Pages 225-245

  6. L p-Solutions of Boundary Value Problems

    • Dagmar Medková
    Pages 247-385

  7. Classical Solutions of BVP

    • Dagmar Medková
    Pages 387-471

  8. Solutions in Sobolev and Besov Spaces

    • Dagmar Medková
    Pages 473-651

  9. Back Matter

    Pages 653-660
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Keywords

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.

Reviews

“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)

Authors and Affiliations

  • Institute of Mathematics of the Czech, Academy of Sciences, Praha 1, Czech Republic

    Dagmar Medková

About the author

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

Bibliographic Information

  • Book Title: The Laplace Equation

  • Book Subtitle: Boundary Value Problems on Bounded and Unbounded Lipschitz Domains

  • Authors: Dagmar Medková

  • DOI: https://doi.org/10.1007/978-3-319-74307-3

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG, part of Springer Nature 2018

  • Hardcover ISBN: 978-3-319-74306-6Published: 13 April 2018

  • Softcover ISBN: 978-3-030-08961-0Published: 14 December 2018

  • eBook ISBN: 978-3-319-74307-3Published: 31 March 2018

  • Edition Number: 1

  • Number of Pages: XIII, 655

  • Topics: Partial Differential Equations, Potential Theory

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