The regularity problem for elliptic operators with boundary data in Hardy-Sobolev space $HS^1$

Details The regularity problem for elliptic operators with boundary data in Hardy-Sobolev space $HS^1$ The regularity problem for elliptic operators with boundary data in Hardy-Sobolev space $HS^1$

2011-10-24

arxiv.org/abs/1110.5189v1

Mathematics

Analysis of PDEs

20 pages

Scientific paper

Let $\Omega$ be a Lipschitz domain in $\mathbb R^n,n\geq 3,$ and $L=\divt A\nabla$ be a second order elliptic operator in divergence form. We will establish that the solvability of the Dirichlet regularity problem for boundary data in Hardy-Sobolev space $\HS$ is equivalent to the solvability of the Dirichlet regularity problem for boundary data in $H^{1,p}$ for some $1

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