N. A. Gusev

activity

20242026

collaborators

5 papers

math.AP2026

On flows generated by square-integrable vector fields

Nikolay A. Gusev, Mikhail V. Korobkov, Evgeny Yu. Panov +1

For square-integrable divergence-free vector field $v$ on $R^{d}$ we prove that the following properties are equivalent: 1) the operator $A_0 ρ= \boldsymbol{v}…

math.AP2026

On chain rule and renormalization

Roman V. Dribas, Nikolay A. Gusev

We discuss the relationship between the chain rule for the divergence operator and the renormalization property for weak solutions of the continuity equation. We construct an examp…

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…