Global regularity estimates for non-divergence elliptic equations on weighted variable Lebesgue spaces

The Quan Bui; The Anh Bui; Xuan Thinh Duong

doi:10.1142/S0219199720500145

Global regularity estimates for non-divergence elliptic equations on weighted variable Lebesgue spaces

The Quan Bui, The Anh Bui^*, Xuan Thinh Duong^*

^*Corresponding author for this work

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

13 Citations (Scopus)

Abstract

This paper is to prove global regularity estimates for solutions to the second-order elliptic equation in non-divergence form with BMO coefficients in a C^1,1 domain on weighted variable exponent Lebesgue spaces. Our approach is based on the representations for the solutions to the non-divergence elliptic equations and the domination technique by sparse operators in harmonic analysis.

Original language	English
Article number	2050014
Pages (from-to)	2050014-1-2050014-26
Number of pages	26
Journal	Communications in Contemporary Mathematics
Volume	23
Issue number	5
Early online date	10 Mar 2020
DOIs	https://doi.org/10.1142/S0219199720500145
Publication status	Published - Aug 2021

Keywords

Non-divergence elliptic equation
weighted variable exponent Lebesgue space
bounded mean oscillation (BMO) space

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10.1142/S0219199720500145

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title = "Global regularity estimates for non-divergence elliptic equations on weighted variable Lebesgue spaces",

abstract = "This paper is to prove global regularity estimates for solutions to the second-order elliptic equation in non-divergence form with BMO coefficients in a C1,1 domain on weighted variable exponent Lebesgue spaces. Our approach is based on the representations for the solutions to the non-divergence elliptic equations and the domination technique by sparse operators in harmonic analysis.",

keywords = "Non-divergence elliptic equation, weighted variable exponent Lebesgue space, bounded mean oscillation (BMO) space",

author = "Bui, {The Quan} and Bui, {The Anh} and Duong, {Xuan Thinh}",

year = "2021",

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AU - Bui, The Anh

AU - Duong, Xuan Thinh

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N2 - This paper is to prove global regularity estimates for solutions to the second-order elliptic equation in non-divergence form with BMO coefficients in a C1,1 domain on weighted variable exponent Lebesgue spaces. Our approach is based on the representations for the solutions to the non-divergence elliptic equations and the domination technique by sparse operators in harmonic analysis.

AB - This paper is to prove global regularity estimates for solutions to the second-order elliptic equation in non-divergence form with BMO coefficients in a C1,1 domain on weighted variable exponent Lebesgue spaces. Our approach is based on the representations for the solutions to the non-divergence elliptic equations and the domination technique by sparse operators in harmonic analysis.

KW - Non-divergence elliptic equation

KW - weighted variable exponent Lebesgue space

KW - bounded mean oscillation (BMO) space

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UR - http://purl.org/au-research/grants/arc/DP190100970

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Global regularity estimates for non-divergence elliptic equations on weighted variable Lebesgue spaces

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Keywords

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Harmonic analysis: function spaces and partial differential equations

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Global regularity estimates for non-divergence elliptic equations on weighted variable Lebesgue spaces

Abstract

Keywords

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Other files and links

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Projects

Harmonic analysis: function spaces and partial differential equations

Cite this