Lp spectral independence of elliptic operators via commutator estimates

Matthias Georg Hieber, Elmar Schrohe

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

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
JournalPositivity
Volume3
Issue number3
Publication statusPublished - 1999
Externally publishedYes

Keywords

  • Elliptic systems
  • L spectrum
  • Spectral independence

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis

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