L^∞-Uniqueness of Generalized SCHRÖdinger Operators

2008/01/17 by Ludovic Dan Lemle, Lemle, Ludovic Dan
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Spectral Theory in Mathematical Physics #advanced mathematical theories #math-ph #math.MP #msc:47D03 #msc:47F05. #msc:60J60

paper · pdf · doi:10.48550/arxiv.0801.2755

arxiv created 2008/01/17 · arxiv updated 2009/12/01

Abstract

The main purpose of this paper is to show that the generalized Schrödinger operator \cal A^Vf=1/2Δf+b∇ f-Vf, f∈ C₀^∞(\R^d), is a pre-generator for which we can prove its L^∞(\R^d,dx)-uniqueness. Moreover, we prove the L¹(\R^d,dx)-uniqueness of weak solutions for the Fokker-Planck equation associated with this pre-generator.

Related

• L^∞-uniqueness of Schrödinger operators restricted in an open domain
• L¹-Uniqueness of the Fokker-Planck equation on a Riemannian manifold
• Markov uniqueness and Fokker-Planck-Kolmogorov equations
• Uniqueness for nonlinear Fokker-Planck equations and for McKean-Vlasov SDEs: The degenerate case
• Uniqueness for nonlinear Fokker-Planck equations and weak uniqueness for McKean-Vlasov SDEs