Lp-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 $p\in (\frac{n}{n-1}-\varepsilon,\frac{2n}{n-1}]$ for some $\varepsilon>0$ 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.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Mathematical Modeling in Engineering
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- Journal of Differential Equations
- Volume
- 483
- Pages
- 114681–114681
- Publication date
- 11 August 2026
- Language
- EN