LpL^p solvability of the Stationary Stokes problem on domains with conical singularity in any dimension

preprint2010arXivOpen access

Abstract

The Dirichlet boundary value problem for the Stokes operator with LpL^p data in any dimension on domains with conical singularity (not necessary a Lipschitz graph) is considered. We establish the solvability of the problem for all p∈(2−ε,∞]p\in (2-\varepsilon,\infty] and also its solvability in C(D‾)C(\overline{D}) for the data in C(∂D)C(\partial D)

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