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Lower bounds and Poincaré inequality for the Brezis-Seeger-Van Schaftingen-Yung functionals

  • Nicola Picenni
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Abstract

We consider a family of non-local and non-convex functionals depending on three real parameters (γ,p,λ), which was introduced by H. Brezis, A. Seeger, J. Van Schaftingen and P. L. Yung. In the case γ<−p we prove a lower bound for the Gamma-liminf of these functionals as λ→ 0+ and a Poincaré-type inequality. We also show that such inequality cannot hold if γ>0, and we establish a modified version in this case. These results answer some open questions posed by these authors and by H. M. Nguyen.

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Cite

BibTeXRIS
BibTeX
@misc{picenni2026lower,
  title = {{Lower bounds and Poincaré inequality for the Brezis-Seeger-Van Schaftingen-Yung functionals}},
  author = {Nicola Picenni},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05929},
  eprint = {2610.05929},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05929},
}
RIS
TY  - UNPB
TI  - Lower bounds and Poincaré inequality for the Brezis-Seeger-Van Schaftingen-Yung functionals
AU  - Nicola Picenni
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.05929
UR  - https://arxiv.org/abs/2610.05929
AB  - We consider a family of non-local and non-convex functionals depending on three real parameters (γ,p,λ), which was introduced by H. Brezis, A. Seeger, J. Van Schaftingen and P. L. Yung. In the case γ<−p we prove a lower bound for the Gamma-liminf of these functionals as λ→ 0^+ and a Poincaré-type inequality. We also show that such inequality cannot hold if γ>0, and we establish a modified version in this case. These results answer some open questions posed by these authors and by H. M. Nguyen.
ER  -