$L^p$-solvability of boundary value problems for the Laplacian in locally flat unbounded domains

Abstract

We establish the solvability of the $L^p$-Dirichlet and $L^{p^{\prime }}$-Neumann problems for the Laplacian for $p\in (\frac{n}{n-1}-\epsilon ,\frac{2n}{n-1}]$ for some $\epsilon >0$ in $2$-sided chord-arc domains with unbounded boundary that is sufficiently flat at large scales and outward unit normal vector whose oscillation fails to be small only at finitely many dyadic boundary balls.

Minor corrections and some clarifications. Final version published in Journal of Differential Equations