Differential characterization of quadratic surfaces

Bartłomiej Zawalski

Let $f\in W_{\mathrm{loc}}^{3,1}(\hat{I}\text{c◯})$ be a function defined on a connected open subset $\hat{I}\text{c◯}\subseteq {\mathbb{R}}^2$. We will show that its graph is contained in a quadratic surface if…