On C1 , C2 , and weak type-(1, 1) estimates for linear elliptic operators: part II

Hongjie Dong, Luis Escauriaza, Seick Kim

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9 Citations (Scopus)

Abstract

We extend and improve the results in Dong and Kim (Commun Partial Differ Equ 42(3):417–435, 2017): showing that weak solutions to full elliptic equations in divergence form with zero Dirichlet boundary conditions are continuously differentiable up to the boundary when the leading coefficients have Dini mean oscillation and the lower order coefficients verify certain conditions. Similar results are obtained for non-divergence form equations. We extend the weak type-(1, 1) estimates in Dong and Kim (Commun Partial Differ Equ 42(3):417–435, 2017) and Escauriaza (Duke Math J 74(1):177–201, 1994) up to the boundary and derive a Harnack inequality for non-negative adjoint solutions to non-divergence form elliptic equations, when the leading coefficients have Dini mean oscillation.

Original languageEnglish
Pages (from-to)447-489
Number of pages43
JournalMathematische Annalen
Volume370
Issue number1-2
DOIs
Publication statusPublished - 2018 Feb 1

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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