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Peer-reviewedCC BY 4.0Journal de l'École polytechnique — Mathématiques

Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators

  • Francesca Anceschi
  • Helge Dietert
  • Jessica Guerand
  • Amélie Loher
  • Clément Mouhot
  • Annalaura Rebucci
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Abstract

We propose a systematic approach based on trajectories to prove a Poincaré inequality for weak non-negative sub-solutions to hypoelliptic equations with an arbitrary number of Hörmander commutators, both in the local and in the non-local case. As a consequence, we deduce the weak Harnack inequality and Hölder regularity along the line of the De Giorgi method.

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Cite

BibTeXRIS
BibTeX
@article{anceschi2026poincaré,
  title = {{Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators}},
  author = {Francesca Anceschi and Helge Dietert and Jessica Guerand and Amélie Loher and Clément Mouhot and Annalaura Rebucci},
  journal = {Journal de l'École polytechnique — Mathématiques},
  year = {2026},
  month = aug,
  doi = {10.5802/jep.350},
  eprint = {2401.12194},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05370944v2},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators
AU  - Francesca Anceschi
AU  - Helge Dietert
AU  - Jessica Guerand
AU  - Amélie Loher
AU  - Clément Mouhot
AU  - Annalaura Rebucci
PY  - 2026
DA  - 2026/08/31
JO  - Journal de l'École polytechnique — Mathématiques
DO  - 10.5802/jep.350
UR  - https://hal.science/hal-05370944v2
AB  - We propose a systematic approach based on trajectories to prove a Poincaré inequality for weak non-negative sub-solutions to hypoelliptic equations with an arbitrary number of Hörmander commutators, both in the local and in the non-local case. As a consequence, we deduce the weak Harnack inequality and Hölder regularity along the line of the De Giorgi method.
SN  - 2429-7100
SN  - 2270-518X
ER  -