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A Harnack inequality approach to the interior regularity of parabolic equations. (English) Zbl 0811.35046
From author’s introduction: We prove \(C^{1, \alpha}\) regularity for the evolution \(S(t)\) of surfaces whose normal velocity \(S_ t\) equals to a function of its curvature tensor \(II\), normal vector \(\nu\), position vector \(X\) and time \(t\): \(S_ t - F(II, \nu, X,t) = R(\nu, X,t)\), where the curvature tensor \(II\) is the second fundamental form in the space direction only and \(\nu\) its normal in the space direction. By the compactness arguments \(\dots\) we see that the \(C^{1,\alpha}\) regularity for this equation actually reduces to \(C^{1, \alpha}\) regularity for much simpler equations of the type \(S_ t - F(II, \nu) = 0\).
Reviewer: O.John (Praha)

35K55 Nonlinear parabolic equations
35D10 Regularity of generalized solutions of PDE (MSC2000)
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