Strain and defects in oblique stripe growth

Both the paper and the candidate model solve the same half-space boundary-value problem for ϕ with boundary flux ϕx=g(ϕ), far-field limit ϕ∼kxx+ζ, and 2π-periodicity in ζ. The paper proves existence for all cx≥0, ky>0, strict monotonicity in ζ, uniqueness up to ζ-translation within the monotone class, and a smooth selection map kx=Kx(ky,cx), via a boundary-integral (Dirichlet-to-Neumann) formulation and a homotopy/continuation argument with maximum-principle tools. The model independently derives a boundary fixed-point equation using the DN map, establishes coercivity via the explicit Fourier symbol, obtains a priori bounds and existence via Leray–Schauder, proves strict monotonicity by a weighted maximum principle, and uniqueness by a sliding method. The core claims coincide with the paper’s Theorem 1 and boundary-integral framework, but the proofs differ in machinery and presentation. The model contains minor technical imprecisions (e.g., how compactness is used in the implicit-function step), yet the overall approach aligns with standard PDE tools and the paper’s structure.