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Quantitative maximal Lp-regularity for generators of real contraction semigroups

  • Moritz Egert
  • Jan Giesselmann
  • Marc Hoffmann
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Abstract

Let −A be the generator of a real, symmetric contraction semigroup on a σ-finite measure space. We prove a universal bound for maximal Lp-regularity: In space-time norms |Au|p ≤ (p* + p*/(2(p*−1))) |f|p, where p* = max(p,p/(p−1)) and u is the mild solution to the Cauchy problem with right-hand side f starting at u(0)=0. Linear growth of the constant in p* is optimal. Our proof introduces an elementary approach to maximal regularity that avoids both vector-valued harmonic analysis and dilation theory. We also obtain quantitative maximal regularity estimates for real, non-symmetric semigroups that are contractive on a sector.

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Cite

BibTeXRIS
BibTeX
@misc{egert2026quantitative,
  title = {{Quantitative maximal $\mathrmL^p$-regularity for generators of real contraction semigroups}},
  author = {Moritz Egert and Jan Giesselmann and Marc Hoffmann},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23357},
  eprint = {2610.23357},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23357},
}
RIS
TY  - UNPB
TI  - Quantitative maximal L^p-regularity for generators of real contraction semigroups
AU  - Moritz Egert
AU  - Jan Giesselmann
AU  - Marc Hoffmann
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23357
UR  - https://arxiv.org/abs/2610.23357
AB  - Let −A be the generator of a real, symmetric contraction semigroup on a σ-finite measure space. We prove a universal bound for maximal L^p-regularity: In space-time norms |Au|_p ≤ (p^* + p^*/(2(p^*−1))) |f|_p, where p^* = max(p,p/(p−1)) and u is the mild solution to the Cauchy problem with right-hand side f starting at u(0)=0. Linear growth of the constant in p^* is optimal. Our proof introduces an elementary approach to maximal regularity that avoids both vector-valued harmonic analysis and dilation theory. We also obtain quantitative maximal regularity estimates for real, non-symmetric semigroups that are contractive on a sector.
ER  -