Green's function for nondivergence elliptic operators in two dimensions

Hongjie Dong; Seick Kim

doi:10.1137/20M1323618

Green's function for nondivergence elliptic operators in two dimensions

Hongjie Dong, Seick Kim

Department of Mathematics

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

5 Citations (Scopus)

Abstract

We construct the Green function for second-order elliptic equations in nondivergence form when the mean oscillations of the coefficients satisfy the Dini condition. We show that Green's function is a bounded mean oscillation in the domain and establish logarithmic pointwise bounds. We also obtain pointwise bounds for first and second derivatives of Green's function.

Original language	English
Pages (from-to)	4637-4656
Number of pages	20
Journal	SIAM Journal on Mathematical Analysis
Volume	53
Issue number	4
DOIs	https://doi.org/10.1137/20M1323618
Publication status	Published - 2021

Bibliographical note

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© 2021 Society for Industrial and Applied Mathematics Publications. All rights reserved.

All Science Journal Classification (ASJC) codes

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/20M1323618

Cite this

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abstract = "We construct the Green function for second-order elliptic equations in nondivergence form when the mean oscillations of the coefficients satisfy the Dini condition. We show that Green's function is a bounded mean oscillation in the domain and establish logarithmic pointwise bounds. We also obtain pointwise bounds for first and second derivatives of Green's function.",

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AU - Kim, Seick

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AB - We construct the Green function for second-order elliptic equations in nondivergence form when the mean oscillations of the coefficients satisfy the Dini condition. We show that Green's function is a bounded mean oscillation in the domain and establish logarithmic pointwise bounds. We also obtain pointwise bounds for first and second derivatives of Green's function.

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KW - Green's function

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JF - SIAM Journal on Mathematical Analysis

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Green's function for nondivergence elliptic operators in two dimensions

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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