Abstract
Let {T p:q 1⩽ p⩽ q 2} be a family of consistent C 0 semigroups on L p(Ω), with q 1,q 2 ∈ [1,∞) and Ω ⫅ ℝ open. We show that certain commutator conditions on T p and on the resolvent of its generator A p ensure the p independence of the spectrum of A p for p ∈ [q 1,q 2.
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.
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Hieber, M., Schrohe, E. L p Spectral Independence of Elliptic Operators via Commutator Estimates. Positivity 3, 259–272 (1999). https://doi.org/10.1023/A:1009777826708
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DOI: https://doi.org/10.1023/A:1009777826708