Published Paper

Inserted: 18 sep 2026
Last Updated: 18 sep 2026

Journal: Discrete and Continuous Dynamical Systems
Volume: 59
Pages: 185-202
Year: 2027
Doi: 10.3934/dcds.2026163

Abstract:

We prove a Trudinger--Moser type inequality in fractional Sobolev spaces with singularities on smooth compact sets of codimension $k$, where $1 < k < d$ and $sp = d$. The singular term is given by the inverse $d$-th power of the distance to the submanifold. The proof is based on a fractional Hardy inequality adapted to smooth submanifolds, and we show the sharpness of the constant. We also establish the equivalence of two natural fractional Sobolev spaces vanishing on the singular set.

Keywords: fractional Hardy inequality, Trudinger-type inequality, critical case