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Research Article | Open Access

On some extrapolation in generalized grand Morrey spaces with applications to PDEs

Eteri Gordadze1, Alexander Meskhi1,3, Maria Alessandra Ragusa2,4( )
Andrea Razmadze Mathematical Institute, Ivane Javakhishvili Tbilisi State University, Tbilisi 0193, Georgia
Department of mathematics and computer science, University of Catania, Catania 6-95125, Italy
Kutaisi International University, Kutaisi 4600, Georgia
Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Vietnam
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Abstract

Rubio de Francia's extrapolation in generalized grand Morrey spaces is derived. This result is applied to the investigation of the regularity of solutions for the second order partial differential equations with discontinuous coefficients in the framework of generalized grand Morrey spaces under the Muckenhoupt condition on weights. Density properties for these spaces are also investigated.

Keywords

Grand Morrey spacesweighted extrapolationweighted estimatesregularity of partial differential equations

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Electronic Research Archive
Volume 32 Issue 1,
January 2024
Pages 551-564
DOI: 10.3934/era.2024027

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Cite this article:
Gordadze E, Meskhi A, Ragusa MA. On some extrapolation in generalized grand Morrey spaces with applications to PDEs. Electronic Research Archive, 2024, 32(1): 551-564. https://doi.org/10.3934/era.2024027

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Received: 07 December 2022
Revised: 03 February 2023
Accepted: 10 February 2023
Published: 04 January 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)