2021 Quasilinear elliptic systems with nonlinear physical data
Farah Balaadich, Elhoussine Azroul
J. Integral Equations Applications 33(4): 427-441 (2021). DOI: 10.1216/jie.2021.33.427

Abstract

Using the theory of Young measures, we prove the existence of weak solutions to the following quasilinear elliptic system:

A(u)=f(x)+div σ0(x,u),

where A(u)=div σ(x,u,Du) and fW1LM¯(Ω;m). This problem corresponds to a diffusion phenomenon with a source f in a moving and dissolving substance, where the motion is described by σ0.

Citation

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Farah Balaadich. Elhoussine Azroul. "Quasilinear elliptic systems with nonlinear physical data." J. Integral Equations Applications 33 (4) 427 - 441, 2021. https://doi.org/10.1216/jie.2021.33.427

Information

Received: 4 August 2020; Revised: 12 March 2021; Accepted: 20 April 2021; Published: 2021
First available in Project Euclid: 11 March 2022

MathSciNet: MR4393376
zbMATH: 1491.35171
Digital Object Identifier: 10.1216/jie.2021.33.427

Subjects:
Primary: 35D30 , 35J65 , 46E30

Keywords: Orlicz spaces , quasilinear elliptic systems , weak solutions , Young measures

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.33 • No. 4 • 2021
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