dc.contributor.author
Saari, O.
dc.contributor.author
Wang, H. Y.
dc.contributor.author
Wei, Y. H.
dc.date.accessioned
2025-01-21T08:45:42Z
dc.date.available
2025-01-21T08:45:42Z
dc.date.issued
2024-12-25
dc.identifier.uri
http://hdl.handle.net/2072/480065
dc.description.abstract
We provide sparse estimates for gradients of solutions to divergence form elliptic partial differential equations in terms of the source data. We give a general result of Meyers (or Gehring) type, a result for linear equations with VMO coefficients and a result for linear equations with Dini continuous coefficients. In addition, we provide an abstract theorem conditional on PDE estimates available. The linear results have the full range of weighted estimates with Muckenhoupt weights as a consequence.
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dc.description.sponsorship
O. Saari is supported by Generalitat de Catalunya through the grant 2021-SGR-00087; and by the Spanish State Research Agency MCIN/AEI/10.13039/501100011033, Next Generation EU and by ERDF A way of making Europe through the grants RYC2021-032950-I, RED2022-134784-T, PID2021-123903NB-I00 as well as the Severo Ochoa and Maria de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M) . Y. Wei is supported by the National Natural Science Foundation of China (Grant No. 11871242, 11971060) , and Scientific Research Project of Education Department of Jilin Province (Grant No. JJKH20220964KJ) . Part of the research was carried out during the first author's visit to Jilin University, the group in which he wishes to thank for its kind hospitality. We feel very grateful to anonymous reviewers for their time and valuable suggestions about our manuscript.
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dc.format.extent
25 p.
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dc.relation.ispartof
Journal of Differential Equations
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dc.rights
Attribution-NonCommercial-NoDerivatives 4.0 International
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dc.rights.uri
http://creativecommons.org/licenses/by-nc-nd/4.0/
*
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Elliptic equations
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dc.title
Sparse gradient bounds for divergence form elliptic equations
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dc.type
info:eu-repo/semantics/article
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dc.description.version
info:eu-repo/semantics/acceptedVersion
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dc.identifier.doi
10.1016/j.jde.2024.08.048
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dc.rights.accessLevel
info:eu-repo/semantics/openAccess
