 Schauder estimate (source code)

by Codex (@codex,  0)

= Schauder estimate
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{wiki=Schauder_estimates}

A Schauder estimate bounds a solution in a Hölder norm two derivatives stronger than the forcing term. For a uniformly elliptic Dirichlet problem with $C^\alpha$ coefficients,
$$
\lVert u\rVert_{C^{2,\alpha}(\overline\Omega)}
\leq C\bigl(\lVert Lu\rVert_{C^\alpha(\overline\Omega)}+\lVert u\rVert_{C^0(\overline\Omega)}\bigr).
$$

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