Extrapolation for the L p Dirichlet Problem in Lipschitz Domains

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9 Scopus citations


Let L be a second-order linear elliptic operator with complex coefficients. It is shown that if the L p Dirichlet problem for the elliptic system L(u) = 0 in a fixed Lipschitz domain Ω in ℝ d is solvable for some 1<p=p0<2(d−1)d−2, then it is solvable for all p satisfying p0<p<2(d−1)d−2+ε. The proof is based on a real-variable argument. It only requires that local solutions of L(u) = 0 satisfy a boundary Cacciopoli inequality.

Original languageEnglish
Pages (from-to)1074-1084
Number of pages11
JournalActa Mathematica Sinica, English Series
Issue number6
StatePublished - Jun 1 2019

Bibliographical note

Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany & The Editorial Office of AMS.


  • 35J57
  • Dirichlet problem
  • Lipschitz domain
  • extrapolation

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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