The Neumann Problem and Helmholtz Decomposition in Convex Domains

Details The Neumann Problem and Helmholtz Decomposition in Convex Domains The Neumann Problem and Helmholtz Decomposition in Convex Domains

2010-01-05

arxiv.org/abs/1001.0778v1

Mathematics

Analysis of PDEs

17 pages

Scientific paper

We show that the Neumann problem for Laplace's equation in a convex domain
$\Omega$ with boundary data in $L^p(\partial\Omega)$ is uniquely solvable for
$1fields in $L^p(\Omega, \mathbb{R}^d)$.

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