A priori estimate for non-uniform elliptic equations

Li-Ming Yeh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


A priori estimate for non-uniform elliptic equations with periodic boundary conditions is concerned. The domain considered consists of two sub-regions, a connected high permeability region and a disconnected matrix block region with low permeability. Let ε denote the size ratio of one matrix block to the whole domain. It is shown that in the connected high permeability sub-region, the Hölder and the Lipschitz estimates of the non-uniform elliptic solutions are bounded uniformly in ε. But Hölder gradient estimate and Lp estimate of the second order derivatives of the solutions in general are not bounded uniformly in ε.

Original languageEnglish
Pages (from-to)1828-1849
Number of pages22
JournalJournal of Differential Equations
Issue number4
StatePublished - 15 Feb 2011


  • Matrix block region
  • Non-uniform elliptic equations
  • Permeability

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