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

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 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.

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Hölder estimate, parabolic equations
Mathematical Subject Classification 2010
Primary: 35K10
Received: 6 August 2016
Revised: 8 January 2019
Accepted: 6 October 2019
Published: 17 March 2020
Yuanqi Wang
Department of Mathematics
Stony Brook University
Stony Brook, NY
United States