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This paper derives a Pogorelov type C2 estimate for the Hessian quotient equation, showing regularity in convex viscosity solutions under specific conditions.
In this paper, we derive a Pogorelov type interior C² estimate for the Hessian quotient equation σ ₙ/σ ₖ( D²u) =f. As an application, we show that convex viscosity solutions are regular for k≤ n-3 if u∈ C1,α with α>1-2/n-k or u∈ W2,p with p≥(n-1)(n-k)/2. Both exponents are sharp in view of the example in arXiv:2401.12229.
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Lu et al. (2025) studied this question.
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