L^p Maximal regularity for vector-valued Schrödinger operators

2023/12/31 by Davide Addona, Addona, Davide, Vincenzo Leone +5 · 1 citation
Mathematics · #47D06 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Primary: 35K40 #Secondary: 35J47 #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2401.00479

openalex publication_date 2023/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the vector-valued Schrödinger operator -Δ+ V, where the potential term V is a matrix-valued function whose entries belong to L¹_{\rm loc}(ℝ^d) and, for every x∈ℝ^d, V(x) is a symmetric and nonnegative definite matrix, with non positive off-diagonal terms and with eigenvalues comparable each other. For this class of potential terms we obtain maximal inequality in L¹(ℝ^d,ℝ^m). Assuming further that the minimal eigenvalue of V belongs to some reverse Hölder class of order q∈(1,∞)∪\∞\, we obtain maximal inequality in L^p(ℝ^d,ℝ^m), for p in between 1 and some q.

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

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