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

Abstract

This is a note on \cite{LSU} and \cite{FS}. 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.

16 pages, no figure, comments are welcome

References in corpus (1)

• Smooth approximations of the Conical Kahler-Ricci flows