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Zbl 0595.35065
DiBenedetto, Emmanuelle; Friedman, Avner
Addendum to "Hölder estimates for nonlinear degenerate parabolic systems". (English)
[J] J. Reine Angew. Math. 363, 217-220 (1985). ISSN 0075-4102; ISSN 1435-5345/e

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 $p>\max \{3/2,2N/(N+2)\}.$ \par The results can be extended to any p satisfying (2), taking for simplicity $f\sp i=0$.

MSC 2000:: *35K65 Parabolic equations of degenerate type
35K55 Nonlinear parabolic equations
35B65 Smoothness of solutions of PDE

Keywords: nonlinear degenerate parabolic systems; Hölder continuity; weak solutions

Citations: Zbl 0527.35038; Zbl 0549.35061

Cited in: Zbl 0907.35033

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