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

Martin Dindoš; Vladimir Maz'ya

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

Analysis of PDEs 2010-08-02 v1

Authors: Martin Dindoš , Vladimir Maz'ya

Abstract

The Dirichlet boundary value problem for the Stokes operator with $L^p$ 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 $p\in (2-\varepsilon,\infty]$ and also its solvability in $C(\overline{D})$ for the data in $C(\partial D)$

Keywords

Stokes problem conical singularity Lp solvability Dirichlet boundary condition elliptic operator

Cite

@article{arxiv.1007.5495,
  title  = {$L^p$ solvability of the Stationary Stokes problem on domains with conical singularity in any dimension},
  author = {Martin Dindoš and Vladimir Maz'ya},
  journal= {arXiv preprint arXiv:1007.5495},
  year   = {2010}
}

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