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PreprintCC BY-NC 4.0HAL

Fundamental solutions to Kolmogorov-Fokker-Planck equations with unbounded lower order terms

  • Pascal Auscher
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Abstract

We continue the study of fundamental solutions for equations involving Kolmogorov-Fokker-Planck operators with rough local or non-local diffusions. Here we consider possibly unbounded lower order terms, such as drifts and potentials. We prove existence and uniqueness of weak solutions and of an appropriate notion of fundamental solution for a wide class of kinetic equations. This is based on kinetic transfer of regularity and anisotropic embeddings.

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Cite

BibTeXRIS
BibTeX
@misc{auscher2026fundamental,
  title = {{Fundamental solutions to Kolmogorov-Fokker-Planck equations with unbounded lower order terms}},
  author = {Pascal Auscher},
  howpublished = {HAL},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02886},
  eprint = {2611.02886},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05847161v1},
  note = {CC BY-NC 4.0},
}
RIS
TY  - UNPB
TI  - Fundamental solutions to Kolmogorov-Fokker-Planck equations with unbounded lower order terms
AU  - Pascal Auscher
PY  - 2026
DA  - 2026/11/01
PB  - HAL
DO  - 10.48550/arxiv.2611.02886
UR  - https://hal.science/hal-05847161v1
AB  - We continue the study of fundamental solutions for equations involving Kolmogorov-Fokker-Planck operators with rough local or non-local diffusions. Here we consider possibly unbounded lower order terms, such as drifts and potentials. We prove existence and uniqueness of weak solutions and of an appropriate notion of fundamental solution for a wide class of kinetic equations. This is based on kinetic transfer of regularity and anisotropic embeddings.
ER  -