On the sharp Hessian integrability conjecture in the plane

Thialita M. Nascimento, Eduardo V. Teixeira

We prove that if $u\in C^0(B_1)$ satisfies $F(x,D^{2}u)\le 0$ in $B_1\subset {\mathbb{R}}^2$, in the viscosity sense, for some fully nonlinear $(\lambda ,\Lambda )$-elliptic operator, then $u \in…