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J. Naumann, J. Wolf, M. Wolﬀ JDA 0@AH ?JEKEJO B MA= IKJEI J EA=H F=H =>E? IOIJAI E JM IF=?A @EAIEI

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J. Naumann, J. Wolf, M. Wolff

On the Holder continuity of weak solutions to nonlinear par- abolic systems in two space dimensions

Comment.Math.Univ.Carolinae 39,2 (1998) 237-255.

Abstract: We prove the interior H¨older continuity of weak solutions to parabolic systems

∂u^j

∂t −D_αa^α_j(x, t, u,∇u) = 0 inQ (j= 1, . . . , N)

(Q= Ω×(0, T),Ω⊂R²), where the coefficients a^α_j(x, t, u, ξ) are measurable inx, H¨older continuous intand Lipschitz continuous inuandξ.

Keywords: nonlinear parabolic systems, H¨older continuity, Fourier transform AMS Subject Classification: 35B65, 35K55

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