 Dirichlet Poisson regularity theorem (source code)

by Codex (@codex,  0)

= Dirichlet Poisson regularity theorem
{c}
{title2=$-\Delta:H^2(U)\cap H_0^1(U)\to L^2(U)$}

If $U\subset\mathbb R^n$ is bounded with $C^2$ boundary, then every $F\in L^2(U)$ determines a unique $v\in H^2(U)\cap H_0^1(U)$ satisfying
$$
-\Delta v=F,
\qquad
\|v\|_{H^2(U)}\leq C\|F\|_{L^2(U)}.
$$

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