Boundary Value Problems for Second‐Order Elliptic Operators Satisfying a Carleson Condition |
| |
| Authors: | Martin Dindo? Jill Pipher David Rule |
| |
| Institution: | 1. School of Mathematics The University of Edinburgh and Maxwell Institute of Mathematical Sciences James Clerk Maxwell Building, United Kingdom;2. Department of Mathematics Brown University, Providence, RI, USA;3. Department of Mathematics Link?ping University, Linkóping, Sweden |
| |
| Abstract: | Let Ω be a Lipschitz domain in  , and  be a second‐order elliptic operator in divergence form. We establish the solvability of the Dirichlet regularity problem with boundary data in  and of the Neumann problem with  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 Dindo?, Petermichl, and Pipher (2007), where the  Dirichlet problem was considered under the same assumptions, and Dindo? and Rule (2010), where the regularity and Neumann problems were considered on two‐dimensional domains.© 2016 Wiley Periodicals, Inc. |
| |
| Keywords: | |
|
|
