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Addendum to ”Hölder estimates for nonlinear degenerate parabolic systems”. (English) Zbl 0595.35065
In our papers [ibid. 349, 83-128 (1984; Zbl 0527.35038) and ibid. 357, 1- 22 (1985; Zbl 0549.35061)] we established continuity and Hölder continuity for the spatial gradient of weak solutions of $$ (1)\quad \partial u\sp i/\partial t-div(\vert \nabla u\vert\sp{p-2} \nabla u\sp i)=f\sp i\quad (i=1,2,...,m). $$ We claimed that these results hold not only for $p\ge 2$ but also for $$ (2)\quad \max \{1,2N/(N+2)\}<p<2. $$ Because of computational oversight (the coefficient of the first term of (iii) p. 87 of the first paper is (p-2)/4 instead of (p-2)/2, as pointed out by Chen Yazhe), the calculations are valid only for $p>\max \{3/2,2N/(N+2)\}.$ The results can be extended to any p satisfying (2), taking for simplicity $f\sp i=0$.

35K65Parabolic equations of degenerate type
35K55Nonlinear parabolic equations
35B65Smoothness and regularity of solutions of PDE
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