Title: Boundary value problems for the Stokes system in arbitrary Lipschitz domains
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.
Subjects: Boundary value problems, Elliptic Differential equations