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Trudinger-Moser type inequality in fractional Sobolev space with singularity on smooth submanifold

  • Vivek Sahu
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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.

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Cite

BibTeXRIS
BibTeX
@misc{sahu2026trudingermoser,
  title = {{Trudinger-Moser type inequality in fractional Sobolev space with singularity on smooth submanifold}},
  author = {Vivek Sahu},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2606.18182},
  eprint = {2606.18182},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.18182},
}
RIS
TY  - UNPB
TI  - Trudinger-Moser type inequality in fractional Sobolev space with singularity on smooth submanifold
AU  - Vivek Sahu
PY  - 2026
DA  - 2026/08/27
PB  - arXiv
DO  - 10.48550/arxiv.2606.18182
UR  - https://arxiv.org/abs/2606.18182
AB  - 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.
ER  -