CALDERÓN-ZYGMUND ESTIMATES FOR PARABOLIC p(x, t)-LAPLACIAN SYSTEMS
نویسندگان
چکیده
We prove local Calderón-Zygmund estimates for weak solutions of the evolutionary p(x, t)-Laplacian system ∂tu− div ( a(x, t)|Du|p(x,t)−2Du ) = div ( |F |p(x,t)−2F ) under the classical hypothesis of logarithmic continuity for the variable exponent p(x, t). More precisely, we show that the spatial gradient Du of the solution is as integrable as the right-hand side F , i.e. |F |p(·) ∈ Lqloc =⇒ |Du| p(·) ∈ Lqloc for any q > 1 together with quantitative estimates. Thereby, we allow the presence of eventually discontinuous coefficients a(x, t), only requiring a VMO condition with respect to the spatial variable x.
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