Boundary Value Problems for Second‐Order Elliptic Operators Satisfying a Carleson Condition. Issue 7 (13th June 2016) - Dindoš, Martin; Pipher, Jill; Rule, David
Abstract: Let Ω be a Lipschitz domain in ℝ n, n ≥ 2, and L = div A ∇ be a second‐order elliptic operator in divergence form. We establish the solvability of the Dirichlet regularity problem with boundary data in H 1, p ( ∂ Ω ) and of the Neumann problem with L p ( ∂ 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 H 1, p ( ∂ Ω ) Dirichlet problem was considered under the same assumptions, and Dindoš and Rule (2010), where the regularity and Neumann problems were considered on two‐dimensional domains.© 2016 Wiley Periodicals, Inc.