Elliptic systems with measurable coefficients of the type of Lamé system in three dimensions

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We study the 3×3 elliptic systems ∇(a(x)∇×u)-∇(b(x)∇·u)=f, where the coefficients a(x) and b(x) are positive scalar functions that are measurable and bounded away from zero and infinity. We prove that weak solutions of the above system are Hölder continuous under some minimal conditions on the inhomogeneous term f. We also present some applications and discuss several related topics including estimates of the Green's functions and the heat kernels of the above systems.

Original languageEnglish
Pages (from-to)2466-2493
Number of pages28
JournalJournal of Differential Equations
Issue number9
Publication statusPublished - 2011 Nov 1


All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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