Self-improving Property of Nonlinear Higher Order Parabolic Systems near the Boundary
نویسنده
چکیده
We establish global regularity results for a wide class of non-linear higher order parabolic systems. The model problem we have in mind is the parabolic p-Laplacian system of order 2m, m≥ 1, ∂tu+(−1) divm (|Dmu|p−2Dmu) = 0 with prescribed boundary and initial values. We prove that if the boundary values are sufficiently regular, then Dmu is globally integrable to a better power than the natural p. The method also produces a global estimate.
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