Fractional integration and optimal estimates for elliptic systems

Felipe Hernandez; Daniel Spector

doi:10.1007/s00526-024-02722-8

Fractional integration and optimal estimates for elliptic systems

Felipe Hernandez
, Daniel Spector^*

^*此作品的通信作者

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

7 引文斯高帕斯（Scopus）

摘要

In this paper we give an affirmative answer to the Euclidean analogue of a question of Bourgain and Brezis concerning the optimal Lorentz estimate for a Div–Curl system: If F∈L¹(R³;R³) satisfies divF=0 in the sense of distributions, then the function Z=curl(-Δ)^-1F satisfies (Formula presented.) and there exists a constant C>0 such that (Formula presented.) Our proof relies on a new endpoint Hardy–Littlewood–Sobolev inequality for divergence free measures which we obtain via a result of independent interest, an atomic decomposition of such objects.

原文	英語
文章編號	117
期刊	Calculus of Variations and Partial Differential Equations
卷	63
發行號	5
DOIs	https://doi.org/10.1007/s00526-024-02722-8
出版狀態	已發佈 - 2024 6月

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AU - Spector, Daniel

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Y1 - 2024/6

N2 - In this paper we give an affirmative answer to the Euclidean analogue of a question of Bourgain and Brezis concerning the optimal Lorentz estimate for a Div–Curl system: If F∈L1(R3;R3) satisfies divF=0 in the sense of distributions, then the function Z=curl(-Δ)-1F satisfies (Formula presented.) and there exists a constant C>0 such that (Formula presented.) Our proof relies on a new endpoint Hardy–Littlewood–Sobolev inequality for divergence free measures which we obtain via a result of independent interest, an atomic decomposition of such objects.

AB - In this paper we give an affirmative answer to the Euclidean analogue of a question of Bourgain and Brezis concerning the optimal Lorentz estimate for a Div–Curl system: If F∈L1(R3;R3) satisfies divF=0 in the sense of distributions, then the function Z=curl(-Δ)-1F satisfies (Formula presented.) and there exists a constant C>0 such that (Formula presented.) Our proof relies on a new endpoint Hardy–Littlewood–Sobolev inequality for divergence free measures which we obtain via a result of independent interest, an atomic decomposition of such objects.

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JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

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M1 - 117

ER -

Fractional integration and optimal estimates for elliptic systems

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