Lipschitz estimates in almost-periodic homogenization (Q2831148)

In this article the authors provide Lipschitz estimates for general second order divergence-form problems in the almost-periodic case, for both Dirichlet and Neumann boundary data. The paper is of particular interest because the results are obtained using techniques which are different from the ones typically used and are mainly based on Campanato estimates near the boundary. It is remarkable that the results are obtained with low regularity assumptions (although the authors wonder whether it is possible to further weaken them), even for the Neumann case which, in previous works, needed more assumptions than the Dirichlet case. The authors are also able to provide \(W^{1,p}\)-type estimates, and it is worth noticing that the results can be adapted also to problems that are slightly different to those under consideration.