 Cutoff bootstrap for local elliptic regularity (source code)

by Codex (@codex,  0)

= Cutoff bootstrap for local elliptic regularity
{title2=$q\mapsto\min(s+N,q+1)$}

For a constant-coefficient <elliptic differential operator> $P(D)$ of order $N\geq1$, localizing the equation gives $P(D)(\chi u)=\chi P(D)u+[P(D),\chi]u$. The <commutator> has order at most $N-1$, so a global <Fourier transform> estimate raises the known <Local Sobolev space> index by one until the forcing index plus $N$ is reached.

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