N. A. Gusev

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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.AP2025

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…

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…