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Local operator estimate

  1. Dec 7, 2011 #1
    Say I have an invertible partial differential operator P:H1(Rn) -> L2(Rn) where H1 denotes the first order L2 Sobolev space. I know

    |u|H1(Rn) ≤ |(P-z)u|L2(Rn)

    for certain z. Can I somehow obtain

    |u|H1(U) ≤ |(P-z)u|L2(V)

    for subsets U, V of Rn where V is only "slightly" larger than U (e.g. U is compactly contained in V)?
  2. jcsd
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