Astérisque 2012; 241 pp; softcover Number: 344 ISBN10: 2856293433 ISBN13: 9782856293430 List Price: US$75 Member Price: US$60 Order Code: AST/344
 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 BesovTriebelLizorkin spaces, and (6) the Poisson problem with Neumann condition in BesovTriebelLizorkin 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 BesovTriebelLizorkin spaces. Table of Contents  Introduction
 Smoothness spaces and Lipschitz domains
 Rellich identities for divergence form, secondorder 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
