The Laplace Equation

Boundary Value Problems on Bounded and Unbounded Lipschitz Domains
1. Auflage 2018
ISBN: 978-3-319-74306-6
Verlag: Springer International Publishing

Buch, Englisch, 655 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1168 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Medková, Dagmar

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Introduction.- 1 Preliminaries.- 2 Harmonic Functions.- 3 Solutions of the Poisson equation.- 4 PWB solutions of the Dirichlet problem.- 5 Lp-solutions of boundary value problems.- 6 Classical solutions of BVP.- 7 Solutions in Sobolev and Besov spaces.

Über Autor(innen)

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