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Abstract
Let Ω be a Lipschitz domain in Rn,n≥3, andL=\divtA∇ be a second order elliptic operator indivergence form. We will establish that the solvability of theDirichlet regularity problem for boundary data in Hardy–Sobolevspace \HS is equivalent to the solvability of the Dirichletregularity problem for boundary data in H1,p for some1<p<∞. This is a “dual result” to a theorem in \cite{DKP09}, where it has been shown that the solvability of theDirichlet problem with boundary data in BMO is equivalentto the solvability for boundary data in Lp(∂Ω) forsome 1<p<∞.
Original language  English 

Pages (fromto)  699717 
Journal  Mathematical research letters 
Volume  19 
Issue number  3 
DOIs  
Publication status  Published  2012 
Keywords
 math.AP
 35J25
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Dive into the research topics of 'The regularity problem for elliptic operators with boundary data in Hardy–Sobolev space HS'. Together they form a unique fingerprint.Projects
 1 Finished

Solving partial differential equations and systems by techniques of harmonic analysis.
1/12/07 → 30/11/10
Project: Research