Lp spectral independence of elliptic operators via commutator estimates

Matthias Georg Hieber*, Elmar Schrohe

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


Let {Tp : q1 ≤ p ≤ q2} be a family of consistent C0 semigroups on Lp(Ω), with q1, q2 ∈ [1, ∞) and Ω ⊆ ℝn open. We show that certain commutator conditions on Tp and on the resolvent of its generator Ap ensure the p independence of the spectrum of Ap for p ∈ [q1, q2]. Applications include the case of Petrovskij correct systems with Hölder continuous coefficients, Schrödinger operators, and certain elliptic operators in divergence form with real, but not necessarily symmetric, or complex coefficients.

Original languageEnglish
Pages (from-to)259-272
Number of pages14
Issue number3
Publication statusPublished - 1999
Externally publishedYes


  • Elliptic systems
  • L spectrum
  • Spectral independence

ASJC Scopus subject areas

  • General Mathematics
  • Analysis


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