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arXiv · 2407.10863

Fractional Hardy inequality with singularity on submanifold

Adimurthi·Prosenjit Roy·Vivek Sahu
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Abstract

We establish fractional Hardy inequality on bounded domains in $\mathbb{R}^{d}$ with inverse of distance function from smooth boundary of codimension $k$, where $k=2, \dots,d$, as weight function. The case $sp=k$ is the critical case, where optimal logarithmic corrections are required. All the other cases of $sp k$ are also addressed.

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Adimurthi, Prosenjit Roy, Vivek Sahu. 2024-07-15. Fractional Hardy inequality with singularity on submanifold. https://doi.org/10.1007/s00526-025-03221-0

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