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

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2020 by IJMTT Journal
Volume-66 Issue-2
Year of Publication : 2020
Authors : El Houcine RAMI, Abdelkrim BARBARA, Elhoussine AZROUL
  10.14445/22315373/IJMTT-V66I2P503

MLA

MLA Style: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 66.2 (2020):15-36. 

APA Style: El Houcine RAMI, Abdelkrim BARBARA, Elhoussine AZROUL(2020).Existence of a weak solution of some quasilinear elliptical system in a weighted Sobolev space International Journal of Mathematics Trends and Technology, 15-36.

Abstract
We consider, for a bounded open domain Ω in IRand 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* , IR) 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.

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Keywords
Quasilinear Elliptical, solution, Sobolev