 Regularity gain for one plus an even power of the Laplacian

ID: regularity-gain-for-one-plus-an-even-power-of-the-laplacian

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

(Δ^{m} + 1) u = f

distributionally on

R^{n}

m

is even, and

f \in H^{r}

, then

u (ξ) = \frac{f ( ξ )}{1 + ∣ ξ ∣ ^{2 m}}

and

u \in H^{r + 2 m} (R^{n})

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