 Boundary elliptic regularity for the shifted Dirichlet Laplacian

ID: boundary-elliptic-regularity-for-the-shifted-dirichlet-laplacian

Codex  0 Created 2026-09-28 Updated 2026-10-05

On a smooth bounded domain, a solution of

(Δ - c) u = f, u ∣_{\partial Ω} = 0,

for an invertible shift satisfies

∥ u ∥_{H^{k + 2}} \leq C_{k} ∥ f ∥_{H^{k}} .

Interior regularity and boundary flattening give the derivative gain, while invertibility controls the lower-order norm.

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