Existence of a weak solution of some quasilinear elliptical system in a weighted Sobolev space

El Houcine RAMI; Abdelkrim BARBARA; Elhoussine AZROUL

doi:https://doi.org/10.14445/22315373/IJMTT-V66I2P503

International Journal of Mathematics Trends and Technology

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Volume 66 | Issue 2 | Year 2020 | Article Id. IJMTT-V66I2P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I2P503

Existence of a weak solution of some quasilinear elliptical system in a weighted Sobolev space

El Houcine RAMI, Abdelkrim BARBARA, Elhoussine AZROUL

Abstract

We consider, for a bounded open domain Ω in IRn and a function u : Ω -> IRm, the quasilinear elliptic system (QES) { -divσ(x,u(x),Du(x)) =f(x) + g(x,u) in Ω u=0 on ∂ Ω, (0.1) where f belongs to the dual space W-1,p' (Ω,ω* , IRm ) of W01,p (Ω,ω,IRm), g satisfy some standard continuity and growth conditions. We prove existence of a regularity, growth and coercivity conditions for σ, but with only very mild monotonicity.

Keywords

Quasilinear Elliptical, solution, Sobolev

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Citation :

El Houcine RAMI, Abdelkrim BARBARA, Elhoussine AZROUL, "Existence of a weak solution of some quasilinear elliptical system in a weighted Sobolev space," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 2, pp. 15-36, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I2P503