Flux-Hardy Inequalities with Optimal Constants via Divergence and Rearrangements
1 Department of Mathematics and Statistics, Kwara State University Malete, Nigeria
2 Department of Mathematics, University of Ilorin, Nigeria
3 Department of Mathematics, University of Ilorin, Ilorin, Nigeria
* Corresponding author: musiliudeen.anise@kwasu.edu.ng
2 Department of Mathematics, University of Ilorin, Nigeria
3 Department of Mathematics, University of Ilorin, Ilorin, Nigeria
* Corresponding author: musiliudeen.anise@kwasu.edu.ng
Abstract
We develop sharp Hardy-type inequalities for boundary flux functionals generated by dilations of a fixed smooth set in R
n. The
method combines the divergence theorem with rearrangement
bounds to reduce flux estimates to one-dimensional Hardy averages. Directional, divergence-form, and multi-flux inequalities are
obtained in arbitrary dimension with the optimal constant
p
p−1
p
,
and sharpness is shown by explicit near-extremizing constructions
Keywords
Hardy inequality
Divergence theorem
Sharp constant
Rearrangements
flux functional & dilation families
How to Cite
Anise, M. A., Soleye, S. L., & Rauf, K. (2024). Flux-Hardy Inequalities with Optimal Constants via Divergence and Rearrangements. Nigerian Journal of Mathematics and Applications, 34(1), 40-47. https://doi.org/10.67897/njma.2024.huzbmlro
M. A. Anise, S. L. Soleye, and K. Rauf, "Flux-Hardy Inequalities with Optimal Constants via Divergence and Rearrangements," Nigerian Journal of Mathematics and Applications, vol. 34, no. 1, pp. 40-47, June 2024. doi: 10.67897/njma.2024.huzbmlro
