Ikemefuna Agbanusi

collaborators

4 papers

math.CA2025

Banach's Indicatrix Reloaded

Ikemefuna Agbanusi

Banach famously related the smoothness of a function to the size of its level sets. More precisely, he showed that a continuous function is of bounded variation exactly when its "i…

math.CA2025

A Comparison of Bessel and Riesz Potentials

Ikemefuna Agbanusi

How large is the Bessel potential, $G_{I^\pm, I^¼} f$ , compared to the Riesz potential, $I_{I^} \pm f$ ? In this paper, we show that if $I_{I^} \pm f \in L^{p}$ with $0 < I^\pm < 1$ and $p > 1$ , then the following…

math.AP2025

A Note on Moser Iteration and the Large Coupling Limit

Ikemefuna Agbanusi

We consider heat semigroups of the form $exp (t (I^ - I^» 1_{I^c ◯_{0}}))$ on bounded domains. These singularly perturbed equations arise in certain models of diffusion limited che…

math.CA2025

On the Smoothness of Zero-Extensions

Ikemefuna Agbanusi

This note investigates the regularity of zero-extensions of $L^{p}$ functions from bounded domains. Simple examples show the possibility of a loss in smoothness and our goal is to qu…