On the boundary estimates for second-order elliptic equations

M. V. Safonov

doi:10.1080/17476933.2017.1420066

On the boundary estimates for second-order elliptic equations

M. V. Safonov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Consider uniformly elliptic equations in general form Lu = a_ijD_iju + b_iD_iu_i 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 b_i ∈ L^q(Ω),q > n.. The work is presented in a unified way based on a few basic facts from qualitative theory of elliptic equations.

Original language	English (US)
Pages (from-to)	1123-1141
Number of pages	19
Journal	Complex Variables and Elliptic Equations
Volume	63
Issue number	7-8
DOIs	https://doi.org/10.1080/17476933.2017.1420066
State	Published - Aug 3 2018

Bibliographical note

Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

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

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10.1080/17476933.2017.1420066

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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.",

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AU - Safonov, M. V.

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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

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UR - https://www.scopus.com/pages/publications/85041138338#tab=citedBy

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M3 - Article

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VL - 63

SP - 1123

EP - 1141

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

IS - 7-8

ER -

On the boundary estimates for second-order elliptic equations

Abstract

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Keywords

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