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Abstract
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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
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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Keywords
Hölder estimate, parabolic equations
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Mathematical Subject Classification 2010
Primary: 35K10
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Milestones
Received: 6 August 2016
Revised: 8 January 2019
Accepted: 6 October 2019
Published: 17 March 2020
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