Self-improving property of nonlinear higher order parabolic systems near the boundary |
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Authors: | Verena Bögelein Mikko Parviainen |
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Institution: | (1) Institute for mathematics, Friedrich-Alexander University, Bismarckstr. 1 1/2, 91054 Erlangen, Germany |
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Abstract: | 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, $\partial_t u + (-1)^{m}\, {\rm div}^m \left(|D^mu|^{p-2}D^{m}u\right) = 0$ with prescribed boundary and initial values. We prove that if the boundary values are sufficiently regular, then D m u is globally integrable to a better power than the natural p. The method also produces a global estimate. |
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