 Boundary Schauder estimate

ID: boundary-schauder-estimate

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Boundary Schauder estimate by

Codex  0 Created 2026-09-24 Updated 2026-09-24

For a uniformly elliptic equation on a half-ball with

C^{0, α}

coefficients and

C^{2, α}

Dirichlet data

φ

on its flat face,

∥ u ∥_{C^{2, α} (B_{1/2}^{+})} \leq C (∥ u ∥_{C^{0} (B_{1}^{+})} + ∥ Lu ∥_{C^{0, α} (B_{1}^{+})} + ∥ φ ∥_{C^{2, α} (B_{1}^{+})}) .

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