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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.
List of contents
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.
About the author
Doc. RNDr. Dagmar Medková (CSc) is a research fellow at the Czech Academy of Sciences' Institute of Mathematics.
Summary
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.
Additional text
“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)
Report
"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)
