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.
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