On the Calderón-Zygmund Theory for Nonlinear Parabolic Problems with Nonstandard Growth Condition
نویسنده
چکیده
We prove Calderón-Zygmund estimates for a class of parabolic problems whose model is the non-homogeneous parabolic p(x, t)-Laplacian equation ∂tu − div ( |Du|p(x,t)−2Du ) = f − div ( |F|p(x,t)−2F ) . More precisely, we will show that the spatial gradient Du is as integrable as the inhomogeneities f and F, i.e. |F|p(x,t), | f | γ1 γ1−1 ∈ L loc ⇒ |F| p(x,t) ∈ L loc for any q > 1, where γ1 is the lower bound for p(x, t). Moreover, it is possible to use this approach to establish the CalderónZygmund theory for parabolic obstacle problems with p(x, t)-growth.
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تاریخ انتشار 2015