Boundary value problems for the Stokes system in arbitrary Lipschitz domains
By: Marius Mitrea & Matthew Wright
Contributors: Wright, Matt, 1980-; Société mathématique de France
Series: Astérisque -- 344; Astérisque -- 344.
Publisher: Societé mathématique de France
Published: 2012
Place of publication: Paris
Language: eng
Number of pages: 241
ISBN-13: 9782856293430
Subjects: Boundary value problems; Elliptic Differential equations
Description: The goal of this work is to treat the main boundary value problems for the Stokes system, i.e., (i) the Dirichlet problem with Lp-data and nontangential maximal function estimates, (ii) the Neumann problem with Lp-data and nontangential maximal function estimates, (iii) the Regularity problem with Lp1-data and nontangential maximal function estimates, (iv) the transmission problem with Lp-data and nontangential maximal function estimates, (v) the Poisson problem with Dirichlet condition in Besov-Triebel-Lizorkin spaces, (vi) the Poisson problem with Neumann condition in Besov-Triebel-Lizorkin spaces, in Lipschitz domains of arbitrary topology in Rn, for each n [greater than or equal to] 2. Our approach relies on boundary integral methods and yields constructive solutions to the aforementioned problems.
Notes: Revision of Matthew Wright's 2008 Ph. D. dissertation where Marius Mitrea was dissertation supervisor.

Includes bibliographical references.

Abstract also in French.
Table of contents: title: 1. Introduction; title: 2. Smoothness spaces and Lipschitz domains; title: 3. Rellich identities for divergence form, second-order systems; title: 4. The Stokes system and hydrostatic potentials; title: 5. The Lp[superscript] transmission problem with p near 2; title: 6. Local L² estimates; title: 7. The transmission problem in two and three dimensions; title: 8. Higher dimensions; title: 9. Boundary value problems in bounded Lipschitz domains; title: 10. The Poisson problem for the Stokes system; title: 11. Appendix.