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

This book is devoted to boundary value problems of the Laplace equationon bounded and unbounded Lipschitz domains. It studies the Dirichletproblem, the Neumann problem, the Robin problem, the derivativeoblique problem, the transmission problem, the skip problem andmixed problems. It also examines differentsolutions - classical, in Sobolevspaces, in Besov spaces, in homogeneous Sobolev spaces and in thesense of non-tangential limit. It also explains relations betweendifferent solutions.

The book has been written in a way that makes it as readable as possible for a widemathematicalaudience, and includesall the fundamental definitions and propositions from other fields ofmathematics.

This book is of interest to research students, as well as experts in partial differential equations and numerical analysis.