Boundary value problems for the Stokes system in arbitrary Lipschitz domains

Quatrième de couverture

The goal of this work is to treat the main boundary value problems for the Stokes system, i.e.,

(i) the Dirichlet problem with L^p-data and nontangential maximal function estimates,

(ii) the Neumann problem with L^p-data and nontangential maximal function estimates,

(iii) the Regularity problem with L(...)-data and nontangential maximal function estimates,

(iv) the transmission problem with L^p-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 (...)ⁿ, for each n (...) 2. Our approach relies on boundary integral methods and yields constructive solutions to the aforementioned problems.

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