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PreprintCC BY 4.0arXiv

Solutions of the space-fractional heat equation with polynomial growth: Liouville theorems and Schauder estimates

  • Serena Dipierro
  • Ovidiu Savin
  • Enrico Valdinoci
  • Riccardo Villa
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Abstract

With the aim of extending to parabolic equations the framework developed by the first three authors in [Dipierro, Savin, and Valdinoci, Rev. Mat. Iberoam. (2019)], we introduce a notion of (viscosity) solutions for the space-fractional heat equation modulo k. In turn, we are able to define s-caloric functions with polynomial growth at infinity, showing also related Schauder estimates, a Liouville-type result, and a stability property with respect to the L∞loc-convergence.

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Cite

BibTeXRIS
BibTeX
@misc{dipierro2026solutions,
  title = {{Solutions of the space-fractional heat equation with polynomial growth: Liouville theorems and Schauder estimates}},
  author = {Serena Dipierro and Ovidiu Savin and Enrico Valdinoci and Riccardo Villa},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03840},
  eprint = {2611.03840},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03840},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Solutions of the space-fractional heat equation with polynomial growth: Liouville theorems and Schauder estimates
AU  - Serena Dipierro
AU  - Ovidiu Savin
AU  - Enrico Valdinoci
AU  - Riccardo Villa
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03840
UR  - https://arxiv.org/abs/2611.03840
AB  - With the aim of extending to parabolic equations the framework developed by the first three authors in [Dipierro, Savin, and Valdinoci, Rev. Mat. Iberoam. (2019)], we introduce a notion of (viscosity) solutions for the space-fractional heat equation modulo k. In turn, we are able to define s-caloric functions with polynomial growth at infinity, showing also related Schauder estimates, a Liouville-type result, and a stability property with respect to the L^∞_loc-convergence.
ER  -