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Boundary Value Problems for the Stokes System in Arbitrary Lipschitz Domains
Marius Mitrea, University of Missouri at Columbia, MO, and Matthew Wright, Missouri State University, Springfield, MO
A publication of the Société Mathématique de France.
cover
Astérisque
2012; 241 pp; softcover
Number: 344
ISBN-10: 2-85629-343-3
ISBN-13: 978-2-85629-343-0
List Price: US$75
Member Price: US$60
Order Code: AST/344
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The goal of this work is to treat the following main boundary value problems for the Stokes system: (1) the Dirichlet problem with \(L^p\)-data and nontangential maximal function estimates, (2) the Neumann problem with \(L^p\)-data and nontangential maximal function estimates, (3) the Regularity problem with \(L^p_1\)-data and nontangential maximal function estimates, (4) the transmission problem with \(L^p\)-data and nontangential maximal function estimates, (5) the Poisson problem with Dirichlet condition in Besov-Triebel-Lizorkin spaces, and (6) the Poisson problem with Neumann condition in Besov-Triebel-Lizorkin spaces, in Lipschitz domains of arbitrary topology in \({\mathbb{R}}^n\), for each \(n\geq2\).

The authors' approach relies on boundary integral methods and yields constructive solutions to the aforementioned problems.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in the Stokes system, Lipschitz domains, boundary problems, layer potentials, and Besov-Triebel-Lizorkin spaces.

Table of Contents

  • Introduction
  • Smoothness spaces and Lipschitz domains
  • Rellich identities for divergence form, second-order systems
  • The Stokes system and hydrostatic potentials
  • The \(L^p\) transmission problem with \(p\) near 2
  • Local \(L^2\) estimates
  • The transmission problem in two and three dimensions
  • Higher dimensions
  • Boundary value problems in bounded Lipschitz domains
  • The Poisson problem for the Stokes system
  • Appendix
  • Bibliography
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