Interior C² estimate for Hessian quotient equation in general dimension

2024/01/17 by Lu, Siyuan · 1 citation
#35J15 #35J60 #35J96 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.12229

Abstract

In this paper, we study the interior C² regularity problem for the Hessian quotient equation ((σ_n)/(σ_k))(D²u)=f. We give a complete answer to this longstanding problem: for k=n-1,n-2, we establish an interior C² estimate; for k≤ n-3, we show that interior C² estimate fails by finding a singular solution.

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• A special concavity property for positive Hessian quotient operators

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