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Visik, M.I. (1963) Quasi-Linear Strongly Elliptic Systems of Differential Equations of Divergence Form. Trudy Moskov. Mat. Obsc, 12, 125-184. (In Russian)

has been cited by the following article:

• TITLE: Quasilinear Degenerated Elliptic Systems with Weighted in Divergence Form with Weak Monotonicity with General Data

  AUTHORS: Abdelkrim Barbara, El Houcine Rami, Elhoussine Azroul

  KEYWORDS: Quasilinear Elliptic, Sobolev Spaces with Weight, Young Measure, Galerkin Scheme

  JOURNAL NAME: Applied Mathematics, Vol.12 No.6, June 30, 2021

  ABSTRACT: We consider, for a bounded open domain Ω in Rn and a function u : Ω → Rm, the quasilinear elliptic system: (1). We generalize the system (QES)(f,g) in considering a right hand side depending on the jacobian matrix Du. Here, the star in (QES)(f,g) indicates that f may depend on Du. In the right hand side, v belongs to the dual space W-1,P’(Ω, ω*, Rm), , f and 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 assumptions.