On poisson operators and dirichlet-neumann maps in Hs for divergence form elliptic operators with lipschitz coefficients

Yasunori Maekawa, Hideyuki Miura

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We consider second order uniformly elliptic operators of divergence form in Rd+1 whose coefficients are independent of one variable. Under the Lipschitz condition on the coefficients we characterize the domain of the Poisson operators and the Dirichlet-Neumann maps in the Sobolev space Hs(Rd) for each s∈[0,1]. Moreover, we also show a factorizationformula for the elliptic operator in terms of the Poisson operator.

Original languageEnglish
Pages (from-to)6227-6252
Number of pages26
JournalTransactions of the American Mathematical Society
Volume368
Issue number9
DOIs
Publication statusPublished - 2016

Keywords

  • DirichletNeumann maps
  • Divergence form elliptic operators
  • Poisson operators

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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