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

Hongjie Dong, Luis Escauriaza, Seick Kim

Research output: Contribution to journalArticle

6 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

Fingerprint

Elliptic Operator
Linear Operator
Elliptic Equations
Coefficient
Estimate
Oscillation
Partial
Harnack Inequality
Continuously differentiable
Dirichlet Boundary Conditions
Weak Solution
Divergence
Non-negative
Verify
Zero
Form

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Dong, Hongjie ; Escauriaza, Luis ; Kim, Seick. / On C1 , C2 , and weak type-(1, 1) estimates for linear elliptic operators : part II. In: Mathematische Annalen. 2018 ; Vol. 370, No. 1-2. pp. 447-489.
@article{39f570b73d624df2b7db6e0671dd213c,
title = "On C1 , C2 , and weak type-(1, 1) estimates for linear elliptic operators: part II",
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.",
author = "Hongjie Dong and Luis Escauriaza and Seick Kim",
year = "2018",
month = "2",
day = "1",
doi = "10.1007/s00208-017-1603-6",
language = "English",
volume = "370",
pages = "447--489",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer New York",
number = "1-2",

}

On C1 , C2 , and weak type-(1, 1) estimates for linear elliptic operators : part II. / Dong, Hongjie; Escauriaza, Luis; Kim, Seick.

In: Mathematische Annalen, Vol. 370, No. 1-2, 01.02.2018, p. 447-489.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On C1 , C2 , and weak type-(1, 1) estimates for linear elliptic operators

T2 - part II

AU - Dong, Hongjie

AU - Escauriaza, Luis

AU - Kim, Seick

PY - 2018/2/1

Y1 - 2018/2/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85031087900&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85031087900&partnerID=8YFLogxK

U2 - 10.1007/s00208-017-1603-6

DO - 10.1007/s00208-017-1603-6

M3 - Article

AN - SCOPUS:85031087900

VL - 370

SP - 447

EP - 489

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 1-2

ER -