A "nonlinear duality" approach to $ W_0^{1, 1} $ solutions in elliptic systems related to the Keller-Segel model

Lucio Boccardo; Lucio Boccardo

doi:10.3934/mine.2023085

Mathematics in Engineering

2023, Volume 5, Issue 5: 1-11. doi: 10.3934/mine.2023085

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A "nonlinear duality" approach to $ W_0^{1, 1} $ solutions in elliptic systems related to the Keller-Segel model

Lucio Boccardo ^,

Istituto Lombardo – Accademia di Scienze e Lettere - Palazzo di Brera, Milano, Italia

Received: 20 April 2022 Revised: 13 February 2023 Accepted: 05 April 2023 Published: 09 May 2023

In this paper, we prove existence of distributional solutions of a nonlinear elliptic system, related to the Keller-Segel model. Our starting point is the boundedness theorem (for solutions of elliptic equations) proved by Guido Stampacchia and Neil Trudinger.
- duality method,
- nonlinear elliptic system,
- $ W_0^{1, 1} $ solutions
Citation: Lucio Boccardo. A 'nonlinear duality' approach to $ W_0^{1, 1} $ solutions in elliptic systems related to the Keller-Segel model[J]. Mathematics in Engineering, 2023, 5(5): 1-11. doi: 10.3934/mine.2023085

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Abstract

In this paper, we prove existence of distributional solutions of a nonlinear elliptic system, related to the Keller-Segel model. Our starting point is the boundedness theorem (for solutions of elliptic equations) proved by Guido Stampacchia and Neil Trudinger.

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