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

Yuanqi Wang

Vol. 305 (2020), No. 1, 311–328

DOI: 10.2140/pjm.2020.305.311

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

Mathematical Subject Classification 2010

Primary: 35K10

Milestones

Received: 6 August 2016

Revised: 8 January 2019

Accepted: 6 October 2019

Published: 17 March 2020