## Boundary value problems for the Stokes system in arbitrary Lipschitz domains

##### Abstract

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.

##### Degree

Ph. D.