Theoretical analysis demonstrates Lp-solvability for Laplacian Dirichlet and Neumann boundary value problems in unbounded chord-arc domains, expanding classical elliptic PDE theory.
We establish the solvability of the Lᵖ-Dirichlet and Lp^-Neumann problems for the Laplacian for p∈ (n/n-1-ε,2n/n-1] for some ε>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.
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Ignasi Guillén-Mola (2026) studied this question.
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