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Everywhere Hölder continuity of the spatial gradient of weak solutions to nonlinear parabolic systems

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Abstract

We consider weak solutions to the parabolic system ∂u i∂t−D α A α i (∇u)=B i(∇u) in (i=1,...,) (Q=Ω×(0,T), Rn a domain), where the functionsB i may have a quadratic growth. Under the assumptionsn≤2 and ∇u ɛL 4+δloc (Q; RnN) (δ>0) we prove that ∇u is locally Hölder continuous inQ.

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  1. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099, Berlin, Germany

    J. Naumann

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  1. J. Naumann
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Naumann, J. Everywhere Hölder continuity of the spatial gradient of weak solutions to nonlinear parabolic systems. Rend. Circ. Mat. Palermo 47, 409–430 (1998). https://doi.org/10.1007/BF02851389

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  • DOI: https://doi.org/10.1007/BF02851389

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