À propos d'estimations pour des systèmes elliptiques à données L1

Bogdan Raita; Daniel Spector

doi:10.1016/j.crma.2019.11.007

À propos d'estimations pour des systèmes elliptiques à données L¹

Translated title of the contribution: 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.

Translated title of the contribution	A note on estimates for elliptic systems with L¹ data
Original language	French
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

Mathematics(all)

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title = "{\`A} propos d'estimations pour des syst{\`e}mes elliptiques {\`a} donn{\'e}es L1 ",

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",

month = nov,

day = "1",

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

language = "法語",

volume = "357",

pages = "851--857",

journal = "Comptes Rendus Mathematique",

issn = "1631-073X",

publisher = "Elsevier Masson",

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T1 - À propos d'estimations pour des systèmes elliptiques à données L1

AU - Raita, Bogdan

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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U2 - 10.1016/j.crma.2019.11.007

DO - 10.1016/j.crma.2019.11.007

M3 - 期刊論文

AN - SCOPUS:85075738155

SN - 1631-073X

VL - 357

SP - 851

EP - 857

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 11-12

ER -

À propos d'estimations pour des systèmes elliptiques à données L¹

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