Green’s function for second order elliptic equations with singular lower order coefficients

Seick Kim, Georgios Sakellaris

Research output: Contribution to journalArticleResearch

4 Citations (Scopus)

Abstract

© 2018, © 2018 Taylor & Francis Group, LLC. We construct Green’s function for second order elliptic operators of the form (Formula presented.) in a domain and obtain pointwise bounds, as well as Lorentz space bounds. We assume that the matrix of principal coefficients (Formula presented.) is uniformly elliptic and bounded and the lower order coefficients b, c, and d belong to certain Lebesgue classes and satisfy the condition (Formula presented.). In particular, we allow the lower order coefficients to be singular. We also obtain the global pointwise bounds for the gradient of Green’s function in the case when the mean oscillations of the coefficients (Formula presented.) and b satisfy the Dini conditions and the domain is (Formula presented.).
Original languageEnglish
Pages (from-to)228-270
JournalCommunications in Partial Differential Equations
Volume44
DOIs
Publication statusPublished - 4 Mar 2019

Keywords

  • Dini mean oscillation
  • Green’s function
  • Lorentz bounds
  • pointwise bounds
  • singular lower order coefficients

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