Vol. 305, No. 1, 2020

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Remarks on the Hölder-continuity of solutions to parabolic equations with conic singularities

Yuanqi Wang

Vol. 305 (2020), No. 1, 311–328
Abstract

This is a note on work of Ladyzhenskaja et al. (AMS 1968) and of Ferretti and Safonov (2013). Using their work line by line, we prove the Hölder-continuity of solutions to linear parabolic equations of mixed type, assuming the coefficient of $\frac{\partial }{\partial t}$ has time-derivative bounded from above. On a Kähler manifold, this Hölder estimate works when the metrics possess conic singularities along a normal crossing divisor.

Keywords
Hölder estimate, parabolic equations
Primary: 35K10