Compactness methods in the theory of homogenization II: Equations in non‐divergence form

Research output: Contribution to journalArticle

Abstract

We prove C0, α, C1, α and C1, 1 a priori estimates for solutions of boundary value problems for elliptic operators with periodic coefficients of the form Σ in,j=1ai j(x/ϵ)δ2/δxiδxj. The constants in these estimates are independent of the small parameter ϵ, and hence our results imply strengthened versions of the classical averaging theorems. These results generalize to a wide class of linear operators in non‐divergence form, including equations with lower‐order terms and nonuniformly oscillating coefficients, as well as to certain nonlinear problems, which we discuss in the last section.

Original languageEnglish (US)
Pages (from-to)139-172
Number of pages34
JournalCommunications on Pure and Applied Mathematics
Volume42
Issue number2
DOIs
StatePublished - Mar 1989

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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