Schauder estimates for equations with cone metrics, II

Abstract

This is the continuation of our paper \cite{GS}, to study the linear theory for equations with conical singularities. We derive interior Schauder estimates for linear elliptic and parabolic equations with a background K\"ahler metric of conical singularities along a divisor of simple normal crossings. As an application, we prove the short-time existence of the conical K\"ahler-Ricci flow with conical singularities along a divisor with simple normal crossings.