On the boundary estimates for second-order elliptic equations

Research output: Contribution to journalArticle

Abstract

Consider uniformly elliptic equations in general form Lu = aijDiju + biDiui n a domain Ω ⊂ Rn, n ≥ 2.. We discuss the minimal assumptions on the boundary of Ω which guarantee the existence or non-existence of Hopf–Oleinik estimates for solutions, provided bi ∈ Lq(Ω),q > n.. The work is presented in a unified way based on a few basic facts from qualitative theory of elliptic equations.

Original languageEnglish (US)
Pages (from-to)1123-1141
Number of pages19
JournalComplex Variables and Elliptic Equations
Volume63
Issue number7-8
DOIs
StatePublished - Aug 3 2018

Fingerprint

Second Order Elliptic Equations
Elliptic Equations
Estimate
Nonexistence
Form

Keywords

  • 35B45
  • 35J15
  • Elliptic equations
  • Hopf–Oleinik lemma
  • measurable coefficients

Cite this

On the boundary estimates for second-order elliptic equations. / Safonov, Mikhail V.

In: Complex Variables and Elliptic Equations, Vol. 63, No. 7-8, 03.08.2018, p. 1123-1141.

Research output: Contribution to journalArticle

@article{3a2670c7c19c4df1b69d170bbb39f522,
title = "On the boundary estimates for second-order elliptic equations",
abstract = "Consider uniformly elliptic equations in general form Lu = aijDiju + biDiui n a domain Ω ⊂ Rn, n ≥ 2.. We discuss the minimal assumptions on the boundary of Ω which guarantee the existence or non-existence of Hopf–Oleinik estimates for solutions, provided bi ∈ Lq(Ω),q > n.. The work is presented in a unified way based on a few basic facts from qualitative theory of elliptic equations.",
keywords = "35B45, 35J15, Elliptic equations, Hopf–Oleinik lemma, measurable coefficients",
author = "Safonov, {Mikhail V}",
year = "2018",
month = "8",
day = "3",
doi = "10.1080/17476933.2017.1420066",
language = "English (US)",
volume = "63",
pages = "1123--1141",
journal = "Complex Variables and Elliptic Equations",
issn = "1747-6933",
publisher = "Taylor and Francis Ltd.",
number = "7-8",

}

TY - JOUR

T1 - On the boundary estimates for second-order elliptic equations

AU - Safonov, Mikhail V

PY - 2018/8/3

Y1 - 2018/8/3

N2 - Consider uniformly elliptic equations in general form Lu = aijDiju + biDiui n a domain Ω ⊂ Rn, n ≥ 2.. We discuss the minimal assumptions on the boundary of Ω which guarantee the existence or non-existence of Hopf–Oleinik estimates for solutions, provided bi ∈ Lq(Ω),q > n.. The work is presented in a unified way based on a few basic facts from qualitative theory of elliptic equations.

AB - Consider uniformly elliptic equations in general form Lu = aijDiju + biDiui n a domain Ω ⊂ Rn, n ≥ 2.. We discuss the minimal assumptions on the boundary of Ω which guarantee the existence or non-existence of Hopf–Oleinik estimates for solutions, provided bi ∈ Lq(Ω),q > n.. The work is presented in a unified way based on a few basic facts from qualitative theory of elliptic equations.

KW - 35B45

KW - 35J15

KW - Elliptic equations

KW - Hopf–Oleinik lemma

KW - measurable coefficients

UR - http://www.scopus.com/inward/record.url?scp=85041138338&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041138338&partnerID=8YFLogxK

U2 - 10.1080/17476933.2017.1420066

DO - 10.1080/17476933.2017.1420066

M3 - Article

VL - 63

SP - 1123

EP - 1141

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

SN - 1747-6933

IS - 7-8

ER -