A note on estimates for elliptic systems with L1 data

Bogdan Raita; Daniel Spector

doi:10.1016/j.crma.2019.11.007

A note on estimates for elliptic systems with L¹ data

Bogdan Raita, Daniel Spector

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

1 Citation (Scopus)

Abstract

In this paper, we give necessary and sufficient conditions on the compatibility of a kth-order homogeneous linear elliptic differential operator A and differential constraint C for solutions to Au=fsubject toCf=0 in Rⁿ to satisfy the estimates ‖D^k−ju‖_{L^{[Formula presented]}(Rⁿ)}⩽c‖f‖_L¹(Rⁿ) for j∈{1,…,min⁡{k,n−1}} and ‖D^k−nu‖_L^∞(Rⁿ)⩽c‖f‖_L¹(Rⁿ) when k≥n.

Original language	English
Pages (from-to)	851-857
Number of pages	7
Journal	Comptes Rendus Mathematique
Volume	357
Issue number	11-12
DOIs	https://doi.org/10.1016/j.crma.2019.11.007
Publication status	Published - 2019 Nov 1
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1016/j.crma.2019.11.007

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title = "A note on estimates for elliptic systems with L1 data",

abstract = "In this paper, we give necessary and sufficient conditions on the compatibility of a kth-order homogeneous linear elliptic differential operator A and differential constraint C for solutions to Au=fsubject toCf=0 in Rn to satisfy the estimates ‖Dk−ju‖L [Formula presented] (Rn)⩽c‖f‖L1(Rn) for j∈{1,…,min⁡{k,n−1}} and ‖Dk−nu‖L∞(Rn)⩽c‖f‖L1(Rn) when k≥n.",

author = "Bogdan Raita and Daniel Spector",

note = "Publisher Copyright: {\textcopyright} 2019 Acad{\'e}mie des sciences",

year = "2019",

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doi = "10.1016/j.crma.2019.11.007",

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AU - Spector, Daniel

PY - 2019/11/1

Y1 - 2019/11/1

N2 - In this paper, we give necessary and sufficient conditions on the compatibility of a kth-order homogeneous linear elliptic differential operator A and differential constraint C for solutions to Au=fsubject toCf=0 in Rn to satisfy the estimates ‖Dk−ju‖L [Formula presented] (Rn)⩽c‖f‖L1(Rn) for j∈{1,…,min⁡{k,n−1}} and ‖Dk−nu‖L∞(Rn)⩽c‖f‖L1(Rn) when k≥n.

AB - In this paper, we give necessary and sufficient conditions on the compatibility of a kth-order homogeneous linear elliptic differential operator A and differential constraint C for solutions to Au=fsubject toCf=0 in Rn to satisfy the estimates ‖Dk−ju‖L [Formula presented] (Rn)⩽c‖f‖L1(Rn) for j∈{1,…,min⁡{k,n−1}} and ‖Dk−nu‖L∞(Rn)⩽c‖f‖L1(Rn) when k≥n.

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 11-12

ER -

A note on estimates for elliptic systems with L¹ data

Abstract

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