Boundary value problems for second order elliptic operators satisfying a Carleson condition
2015 (English)In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312Article in journal (Refereed) Epub ahead of print
Let be a Lipschitz domain in Rn n ≥ 2, and L = divA∇· be a second order elliptic operator in divergence form. We establish solvability of the Dirichlet regularity problem with boundary data in H1,p(@) and of the Neumann problem with Lp(@) data for the operator L on Lipschitz domains with small Lipschitz con- stant. 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  where the Lp(@) Dirichlet problem was considered under the same assumptions and  where the regularity and Neumann problems were considered on two dimensional domains.
Place, publisher, year, edition, pages
Elliptic equations, Carleson measures, Boundary value problems, Lipschitz domains
IdentifiersURN: urn:nbn:se:liu:diva-125452DOI: 10.1002/cpa.21649OAI: oai:DiVA.org:liu-125452DiVA: diva2:906300