N. A. Gusev

collaborators

3 papers

math.CA2025

Nowhere monotone Riemann integrable derivative without local extrema

Nikolay A. Gusev, Andrey E. Komagorov

We construct a nowhere monotone Riemann integrable derivative which has no local extrema. We also construct a differentiable function $G$ such that $G^{'}$ is Riemann integrable and h…

math.AP2025

On the weak Sard property

Roman V. Dribas, Andrew S. Golovnev, Nikolay A. Gusev

If $f : [0, 1]^{2} \to R$ is of class $C^{2}$ then Sard's theorem implies that $f$ has the following relaxed Sard property: the image under $f$ of the Lebesgue measure rest…

math.AP2024

The Nelson conjecture and chain rule property

Nikolay A. Gusev, Mikhail V. Korobkov

Let $p \geq 1$ and let $v : R^{d} \to R^{d}$ be a compactly supported vector field with $v \in L^{p} (R^{d})$ and $\operatorname{div} \b…