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Schauder estimates for equations with cone metrics, II

Bin Guo and Jian Song

Vol. 17 (2024), No. 3, 757–830

We continue our work on the linear theory for equations with conical singularities. We derive interior Schauder estimates for linear elliptic and parabolic equations with a background Kähler metric of conical singularities along a divisor of simple normal crossings. As an application, we prove the short-time existence of the conical Kähler–Ricci flow with conical singularities along a divisor with simple normal crossings.

conic Kähler metrics, Schauder estimates
Mathematical Subject Classification 2010
Primary: 35J15, 35K10, 35K67
Received: 23 October 2018
Revised: 6 July 2022
Accepted: 11 August 2022
Published: 24 April 2024
Bin Guo
Department of Mathematics
Columbia University
New York, NY
United States
Department of Mathematics & Computer Science
Rutgers University
Newark, NJ
United States
Jian Song
Department of Mathematics
Rutgers University
Piscataway, NJ
United States

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