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- W2963968010 abstract "In this paper we study the constant scalar curvature equation (CSCK), a nonlinear fourth-order elliptic equation, and its weak solutions on Kähler manifolds. We first define the notion of a weak solution of CSCK for an L∞ Kähler metric. The main result is to show that such a weak solution (with uniform L∞ bound) is smooth. As an application, this answers in part a conjecture of Chen regarding the regularity of K-energy minimizers. The new technical ingredient is a W2, 2 regularity result for the Laplacian equation Δgu=f on Kähler manifolds, where the metric has only L∞ coefficients. It is well-known that such a W2, 2 regularity (W2, p regularity for any p > 1) fails in general (except for dimension 2) for uniform elliptic equations of the form for aij ∊ L∞ without certain smallness assumptions on the local oscillation of aij. We observe that the Kähler condition plays an essential role in obtaining a W2, 2 regularity for elliptic equations with only L∞ elliptic coefficients on compact manifolds. © 2017 Wiley Periodicals, Inc." @default.
- W2963968010 created "2019-07-30" @default.
- W2963968010 creator A5017366700 @default.
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- W2963968010 date "2018-12-07" @default.
- W2963968010 modified "2023-09-25" @default.
- W2963968010 title "Constant Scalar Curvature Equation and Regularity of Its Weak Solution" @default.
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- W2963968010 doi "https://doi.org/10.1002/cpa.21790" @default.
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