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PreprintCC BY-NC-ND 4.0arXiv

The L1-realization of an elliptic operator with unbounded coefficients

  • Sallah Eddine Boutiah
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Abstract

We establish an L1-theory for a class of elliptic operators with unbounded coefficients, extending our earlier semigroup generation results and those of Canale--Rhandi--Tacelli to the endpoint p=1. The L1-realization generates a positive analytic C0-semigroup that is compact for every positive time. We characterize the generator domain through weighted estimates and prove consistency with the corresponding Lp-semigroups for 1<p<∞.

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Cite

BibTeXRIS
BibTeX
@misc{boutiah2026l1realization,
  title = {{The $L^1$-realization of an elliptic operator with unbounded coefficients}},
  author = {Sallah Eddine Boutiah},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06659},
  eprint = {2610.06659},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06659},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - The L^1-realization of an elliptic operator with unbounded coefficients
AU  - Sallah Eddine Boutiah
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.06659
UR  - https://arxiv.org/abs/2610.06659
AB  - We establish an L^1-theory for a class of elliptic operators with unbounded coefficients, extending our earlier semigroup generation results and those of Canale--Rhandi--Tacelli to the endpoint p=1. The L^1-realization generates a positive analytic C_0-semigroup that is compact for every positive time. We characterize the generator domain through weighted estimates and prove consistency with the corresponding L^p-semigroups for 1<p<∞.
ER  -