Regularity results in grand variable exponent Morrey spaces and applications

Dali Makharadze; Alexander Meskhi; Maria Alessandra Ragusa; Dali Makharadze; Alexander Meskhi; Maria Alessandra Ragusa

doi:10.3934/era.2025123

Electronic Research Archive

2025, Volume 33, Issue 5: 2800-2814. doi: 10.3934/era.2025123

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Research article

Regularity results in grand variable exponent Morrey spaces and applications

1.
Department of Mathematics, Batumi Shota Rustaveli State University, Batumi 6010, Georgia
2.
Department of Mathematical Analysis, A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, Tbilisi 0193, Georgia
3.
Kutaisi International University, Kutaisi 4600, Georgia
4.
Dipartimento di Matematica e Informatica, Università di Catania, Catania 6-95125, Italy
5.
Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Vietnam

Received: 26 February 2025 Revised: 15 April 2025 Accepted: 30 April 2025 Published: 12 May 2025

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.
- grand variable exponent Morrey spaces,
- commutators,
- Calderón–Zygmund operators,
- elliptic PDEs,
- regularity of solution
Citation: Dali Makharadze, Alexander Meskhi, Maria Alessandra Ragusa. Regularity results in grand variable exponent Morrey spaces and applications[J]. Electronic Research Archive, 2025, 33(5): 2800-2814. doi: 10.3934/era.2025123

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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.

References

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