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Lorentz estimates for a class of nonlinear parabolic systems

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Abstract In this paper we obtain the following local Lorentz estimates B ( | F | ) ∈ L l o c γ , q ⇒ B ( | ∇… Click to show full abstract

Abstract In this paper we obtain the following local Lorentz estimates B ( | F | ) ∈ L l o c γ , q ⇒ B ( | ∇ u | ) ∈ L l o c γ , q for any γ > 1 and 0 q ≤ ∞ of the weak solutions for a class of quasilinear parabolic systems u t − div ( a ( | ∇ u | ) ∇ u ) = div ( a ( | F | ) F ) , where B ( t ) = ∫ 0 t τ a ( τ ) d τ for t ≥ 0 .

Keywords: class nonlinear; lorentz estimates; estimates class; nonlinear parabolic; parabolic systems

Journal Title: Journal of Differential Equations
Year Published: 2019

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