Vector-valued Schrödinger operators on L^p-spaces

2018/02/27 by Markus Kunze, Kunze, M., Abdallah Maichine +3 · 1 citation
Mathematics · #35K40 #47D06 #47D08 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1802.09771

openalex publication_date 2018/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider vector-valued Schrödinger operators of the form div(Q∇ u)-Vu, where 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 an that it is pointwise accretive and that its entries are in L^∞_loc(ℝ^d). Under these assumptions, we prove that a realization of the vector-valued Schrödinger operator generates a C₀-semigroup of contractions in L^p(ℝ^d; ℂ^m). Further properties are also investigated.

Cited by

• L^p-quasicontractiveness and Kernel estimates for semigroups generated by systems of elliptic operators

Related

• L^p-theory for Schrödinger systems
• On a polynomial scalar perturbation of a Schr "odinger system in\n L^p-spaces
• Generation of semigroup for symmetric matrix Schr "odinger operators in\n L^p-spaces
• L^p Maximal regularity for vector-valued Schrödinger operators
• On the L^p-theory of vector-valued elliptic operators