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Bao-Zhi Chu

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Preprint Aug 2026

On Singular Sets of Fully Nonlinear Uniformly Elliptic Equations

For continuous viscosity solutions $u$ of fully nonlinear uniformly elliptic equations $F(D^2 u)=0$, the work of Nadirashvili--Tkachev--Vl\u{a}du\c{t} shows that $u$ need not be $C^2$ in dimensions $n\ge 5$. It is therefore natural to ask how large the set $\operatorname{Sing}(u)$, consisting of points at which $u$ has...

Bao-Zhi Chu · 1 citation · ⚡1
Preprint Sep 2026

Nirenberg's Theorem and Singular Solutions from Traceless Symmetric Matrices

Nirenberg's theorem gives interior $C^{2,\alpha}$ regularity for continuous viscosity solutions of fully nonlinear uniformly elliptic equations $F(D^2u)=0$ in dimension two. In dimensions five and higher, the work of Nadirashvili--Tkachev--Vl\u{a}du\c{t} shows that such solutions need not be $C^2$. We construct a famil...

Bao-Zhi Chu · 0 citations

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