Weighted Hardy inequalities and Ornstein-Uhlenbeck type operators perturbed by multipolar inverse square potentials

2017/08/02 by A. Canale, Canale, A., F. Pappalardo +1
Mathematics · #34G10 #35B25 #35K15 #35K65 #47D03 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math.AP #msc:34G10 #msc:35B25 #msc:35K15 #msc:35K65 #msc:47D03

paper · pdf · doi:10.48550/arxiv.1708.00702

arxiv created 2017/08/02 · openalex publication_date 2017/08/02 · arxiv updated 2017/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give necessary and sufficient conditions for the existence of weak solutions of a parabolic problem corresponding to the Kolmogorov operators perturbed by a multipolar inverse square potential with respect to the Gaussian probability measure which is the unique invariant measure for Ornstein-Uhlenbeck type operators. We state the optimality of the constant and, then, the nonexistence of positive exponentially bounded solutions to the parabolic problem.

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