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PreprintCC BY 4.0HAL

EXISTENCE AND UPPER BOUNDS OF FUNDAMENTAL SOLUTIONS TO KINETIC EQUATIONS WITH ROUGH NON-LOCAL DIFFUSION

  • Pascal Auscher
  • Lukas Niebel
Open at sourcePDFDOICite

Abstract

We study the fundamental solution operators associated to Kolmogorov equations with symmetric non-local diffusion with rough kernels. We prove that these operators are induced by measurable kernels and prove sharp upper bounds in terms of a kinetic profile governed by the interplay of transport and non-local diffusion. Our proof combines the small-jump with loss decomposition of P.-A. Meyer with the ideas of Nash. The proof is purely analytic.

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Cite

BibTeXRIS
BibTeX
@misc{auscher2026existence,
  title = {{EXISTENCE AND UPPER BOUNDS OF FUNDAMENTAL SOLUTIONS TO KINETIC EQUATIONS WITH ROUGH NON-LOCAL DIFFUSION}},
  author = {Pascal Auscher and Lukas Niebel},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06214},
  eprint = {2610.06214},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05771831v2},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - EXISTENCE AND UPPER BOUNDS OF FUNDAMENTAL SOLUTIONS TO KINETIC EQUATIONS WITH ROUGH NON-LOCAL DIFFUSION
AU  - Pascal Auscher
AU  - Lukas Niebel
PY  - 2026
DA  - 2026/10/06
PB  - HAL
DO  - 10.48550/arxiv.2610.06214
UR  - https://hal.science/hal-05771831v2
AB  - We study the fundamental solution operators associated to Kolmogorov equations with symmetric non-local diffusion with rough kernels. We prove that these operators are induced by measurable kernels and prove sharp upper bounds in terms of a kinetic profile governed by the interplay of transport and non-local diffusion. Our proof combines the small-jump with loss decomposition of P.-A. Meyer with the ideas of Nash. The proof is purely analytic.
ER  -