On the extension property of Reifenberg-flat domains
Antoine Lemenant, Emmanouil Milakis, Laura V. Spinolo · Annales Academiae Scientiarum Fennicae Mathematica · 2014
We provide a detailed proof of the fact that any open set whose boundary is sufficiently flat in the sense of Reifenberg is also Jones-flat, and hence it admits an extension operator.We discuss various applications of this property, in particular we obtain L ∞ estimates for the eigenfunctions of the Laplace operator with Neumann boundary conditions.We also compare different ways of measuring the "distance" between two Reifenberg-flat domains.These results are pivotal to the quantitative stability analysis of the spectrum of the Neumann Laplacian performed in [27].