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The Laplace Equation: Boundary Value Problems on Bounded and Unbounded Lipschitz Domains
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The Laplace Equation: Boundary Value Problems on Bounded and Unbounded Lipschitz Domains

The Laplace Equation: Boundary Value Problems on Bounded and Unbounded Lipschitz Domains

Dagmar Medkova

655 pages, parution le 12/04/2018

Résumé

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.

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.

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

Caractéristiques techniques

  PAPIER
Éditeur(s) Springer
Auteur(s) Dagmar Medkova
Parution 12/04/2018
Nb. de pages 655
EAN13 9783319743066

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