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Abstract
Let Ω be a Lipschitz domain in ℝn, n ≥ 2, and L = div A∇· be a secondorder elliptic operator in divergence form. We establish the solvability of the Dirichlet regularity problem with boundary data in H1,p(∂Ω) and of the Neumann problem with Lp(∂Ω) data for the operator L on Lipschitz domains with small Lipschitz constant. We allow the coefficients of the operator L to be rough, obeying a certain Carleson condition with small norm. These results complete the results of Dindoš, Petermichl, and Pipher (2007), where the Lp(∂Ω) Dirichlet problem was considered under the same assumptions, and Dindoš and Rule (2010), where the regularity and Neumann problems were considered on twodimensional domains.
Original language  English 

Pages (fromto)  13161365 
Number of pages  50 
Journal  Communications on Pure and Applied Mathematics 
Volume  70 
Issue number  7 
Early online date  13 Jun 2016 
DOIs  
Publication status  Published  Jul 2017 
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Dive into the research topics of 'Boundary value problems for secondorder elliptic operators satisfying a Carleson condition'. Together they form a unique fingerprint.Projects
 2 Finished

Solvability of elliptic partial differential equations with rough coefficients; the boundary value problems
12/09/12 → 11/09/15
Project: Research

Profiles

Martin Dindos
 School of Mathematics  Personal Chair of harmonic analysis and partial differential
Person: Academic: Research Active