Existence of weak solutions for quasilinear elliptic systems in Orlicz spaces

On Steady Flows of Quasi-Newtonian Fluids in Orlicz–Sobolev Spaces

“…For this reason, the homogeneous Orlicz-Sobolev spaces W 1 0,div L M (Ω; R m ) are a suitable framework to explore the growth assumptions by means of a convex function, namely an Nfunction. Further, we extend the result of [3] to a steady quasi-Newtonian given by (1.1)-(1.3). We will prove the existence of weak solutions for problem (1.1)-(1.3) based on the results of [3,4].…”

“…Further, we extend the result of [3] to a steady quasi-Newtonian given by (1.1)-(1.3). We will prove the existence of weak solutions for problem (1.1)-(1.3) based on the results of [3,4]. The function spaces and notations will be presented in detail in Section 2.…”

“…In [3], the present authors studied the existence of solutions for the quasilinear elliptic system (1.4) in Orlicz-Sobolev spaces by using the Young measure and mild monotonicity assumptions on σ. See also [5,6,9] for the unsteady case.…”

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“…For this reason, the homogeneous Orlicz-Sobolev spaces W 1 0,div L M (Ω; R m ) are a suitable framework to explore the growth assumptions by means of a convex function, namely an Nfunction. Further, we extend the result of [3] to a steady quasi-Newtonian given by (1.1)-(1.3). We will prove the existence of weak solutions for problem (1.1)-(1.3) based on the results of [3,4].…”

“…In [3], the present authors studied the existence of solutions for the quasilinear elliptic system (1.4) in Orlicz-Sobolev spaces by using the Young measure and mild monotonicity assumptions on σ. See also [5,6,9] for the unsteady case.…”