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On the Hölder continuity of weak solutions to nonlinear parabolic systems in two space dimensions

Joachim NaumannJörg WolfMichael Wolff — 1998

Commentationes Mathematicae Universitatis Carolinae

We prove the interior Hölder continuity of weak solutions to parabolic systems u j t - D α a j α ( x , t , u , u ) = 0 in Q ( j = 1 , ... , N ) ( Q = Ω × ( 0 , T ) , Ω 2 ), where the coefficients a j α ( x , t , u , ξ ) are measurable in x , Hölder continuous in t and Lipschitz continuous in u and ξ .

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