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

Eteri Gordadze; Alexander Meskhi; Maria Alessandra Ragusa; Eteri Gordadze; Alexander Meskhi; Maria Alessandra Ragusa

doi:10.3934/era.2024027

Electronic Research Archive

2024, Volume 32, Issue 1: 551-564. doi: 10.3934/era.2024027

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Research article

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

1.
Andrea Razmadze Mathematical Institute, Ivane Javakhishvili Tbilisi State University, Tbilisi 0193, Georgia
2.
Department of mathematics and computer science, University of Catania, Catania 6-95125, Italy
3.
Kutaisi International University, Kutaisi 4600, Georgia
4.
Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Vietnam

Received: 07 December 2022 Revised: 03 February 2023 Accepted: 10 February 2023 Published: 04 January 2024

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.
- Grand Morrey spaces,
- weighted extrapolation,
- weighted estimates,
- regularity of partial differential equations
Citation: Eteri Gordadze, Alexander Meskhi, Maria Alessandra Ragusa. On some extrapolation in generalized grand Morrey spaces with applications to PDEs[J]. Electronic Research Archive, 2024, 32(1): 551-564. doi: 10.3934/era.2024027

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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.

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