In this article, we study for p ∈ (1, ∞) the Lp-realization of the vector-valued Schrödinger operator L u := div(Q∇u) + V u. Using a noncommutative version of the Dore–Venni theorem due to Monniaux and Pr ̈uss, we prove that the Lp-realization of L, defined on the intersection of the natural domains of the differential and multiplication operators which form L, generates a strongly continuous contraction semigroup on Lp(R^d; C^m). We also study additional properties of the semigroup such as extension to L1, positivity, ultracontractivity and prove that the generator has compact resolvent.

Lp-theory for Schrödinger systems

Maichine, Abdallah;Rhandi, Abdelaziz
2019-01-01

Abstract

In this article, we study for p ∈ (1, ∞) the Lp-realization of the vector-valued Schrödinger operator L u := div(Q∇u) + V u. Using a noncommutative version of the Dore–Venni theorem due to Monniaux and Pr ̈uss, we prove that the Lp-realization of L, defined on the intersection of the natural domains of the differential and multiplication operators which form L, generates a strongly continuous contraction semigroup on Lp(R^d; C^m). We also study additional properties of the semigroup such as extension to L1, positivity, ultracontractivity and prove that the generator has compact resolvent.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4722152
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