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Research Article | Open Access

Regularity results in grand variable exponent Morrey spaces and applications

Dali Makharadze1( ), Alexander Meskhi2,3, Maria Alessandra Ragusa4,5( )
Department of Mathematics, Batumi Shota Rustaveli State University, Batumi 6010, Georgia
Department of Mathematical Analysis, A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, Tbilisi 0193, Georgia
Kutaisi International University, Kutaisi 4600, Georgia
Dipartimento di Matematica e Informatica, Università di Catania, Catania 6-95125, Italy
Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Vietnam
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Abstract

The boundedness of commutators of Calderón–Zygmund operators in grand variable exponent Morrey spaces is established. The operators and spaces are defined on quasi-metric measure spaces with doubling measure. The obtained results are applied to study regularity properties of solutions of the second-order partial differential equations with discontinuous coefficients in the frame of grand variable exponent Morrey spaces.

Keywords

grand variable exponent Morrey spacescommutatorsCalderón–Zygmund operatorselliptic PDEsregularity of solution

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Electronic Research Archive
Volume 33 Issue 5,
May 2025
Pages 2800-2814
DOI: 10.3934/era.2025123

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Cite this article:
Makharadze D, Meskhi A, Ragusa MA. Regularity results in grand variable exponent Morrey spaces and applications. Electronic Research Archive, 2025, 33(5): 2800-2814. https://doi.org/10.3934/era.2025123

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Received: 26 February 2025
Revised: 15 April 2025
Accepted: 30 April 2025
Published: 15 May 2025
©2025 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)