Existence of solutions to some quasilinear degenerate elliptic systems with right hand side in a Marcinkiewicz space

Patrizia Di Gironimo; Salvatore Leonardi; Francesco Leonetti; Marta Macrì; Pier Vincenzo Petricca; Patrizia Di Gironimo; Salvatore Leonardi; Francesco Leonetti; Marta Macrì; Pier Vincenzo Petricca

doi:10.3934/mine.2023055

Mathematics in Engineering

2023, Volume 5, Issue 3: 1-23. doi: 10.3934/mine.2023055

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Existence of solutions to some quasilinear degenerate elliptic systems with right hand side in a Marcinkiewicz space

1.
Dipartimento di Matematica, Università di Salerno, 84084 Fisciano (SA), Italy
2.
Dipartimento di Matematica e Informatica, Università degli Studi di Catania, 95131 Catania, Italy
3.
Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Università di L'Aquila, 67100 L'Aquila, Italy
4.
Via Sant'Amasio 18, 03039 Sora, Italy

Received: 12 June 2022 Revised: 22 September 2022 Accepted: 29 September 2022 Published: 17 October 2022

We prove the existence of a solution to a quasilinear system of degenerate equations, when the datum is in a Marcinkiewicz space. The main assumption asks the off-diagonal coefficients to have support in the union of a geometric progression of squares.
- degenerate elliptic system,
- Marcinkiewicz space,
- existence of solution
Citation: Patrizia Di Gironimo, Salvatore Leonardi, Francesco Leonetti, Marta Macrì, Pier Vincenzo Petricca. Existence of solutions to some quasilinear degenerate elliptic systems with right hand side in a Marcinkiewicz space[J]. Mathematics in Engineering, 2023, 5(3): 1-23. doi: 10.3934/mine.2023055

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Abstract

We prove the existence of a solution to a quasilinear system of degenerate equations, when the datum is in a Marcinkiewicz space. The main assumption asks the off-diagonal coefficients to have support in the union of a geometric progression of squares.

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