In this paper we consider vector-valued operator div(Q∇u) − V u of Schrödinger type. Here V = (v_{ij}) is a nonnegative locally bounded matrix- valued function and Q is a symmetric, strictly elliptic matrix whose entries are bounded and continuously differentiable with bounded derivatives. Concerning the potential V, we assume that it is pointwise accretive and that its entries are locally bounded and measurable functions in R^d. Under these assumptions, we prove that a realization of the vector-valued Schrödinger operator generates a C_0-semigroup of contractions in Lp(R^d; C^m). Further properties are also investigated.
Vector-valued Schrödinger operators in Lp-spaces
MAICHINE, ABDALLAH;RHANDI, Abdelaziz
2020
Abstract
In this paper we consider vector-valued operator div(Q∇u) − V u of Schrödinger type. Here V = (v_{ij}) is a nonnegative locally bounded matrix- valued function and Q is a symmetric, strictly elliptic matrix whose entries are bounded and continuously differentiable with bounded derivatives. Concerning the potential V, we assume that it is pointwise accretive and that its entries are locally bounded and measurable functions in R^d. Under these assumptions, we prove that a realization of the vector-valued Schrödinger operator generates a C_0-semigroup of contractions in Lp(R^d; C^m). Further properties are also investigated.File in questo prodotto:
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