Details
| Original language | English |
|---|---|
| Pages (from-to) | 259-272 |
| Number of pages | 14 |
| Journal | POSITIVITY |
| Volume | 3 |
| Issue number | 3 |
| Publication status | Published - Sept 1999 |
| Externally published | Yes |
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.
Keywords
- Elliptic systems, L spectrum, Spectral independence
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Theoretical Computer Science
- Mathematics(all)
- General Mathematics
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In: POSITIVITY, Vol. 3, No. 3, 09.1999, p. 259-272.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Lp spectral independence of elliptic operators via commutator estimates
AU - Hieber, Matthias
AU - Schrohe, Elmar
N1 - Copyright: Copyright 2018 Elsevier B.V., All rights reserved.
PY - 1999/9
Y1 - 1999/9
N2 - 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.
AB - 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.
KW - Elliptic systems
KW - L spectrum
KW - Spectral independence
UR - http://www.scopus.com/inward/record.url?scp=22644450486&partnerID=8YFLogxK
U2 - 10.1023/A:1009777826708
DO - 10.1023/A:1009777826708
M3 - Article
AN - SCOPUS:22644450486
VL - 3
SP - 259
EP - 272
JO - POSITIVITY
JF - POSITIVITY
SN - 1385-1292
IS - 3
ER -