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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:463

Article

Canale, Anna¹  Pappalardo, Francesco² 

[1] Univ Salerno, Dipartimento Ingn Informaz & Elettr & Matemat App, Via Giovanni Paolo 2,132, I-84084 Fisciano, SA, Italy

[2] Univ Napoli Federico II, Dipartimento Matemat & Applicaz Renato Caccioppol, Complesso Monte S Angelo,Via Cintia, I-80126 Naples, Italy

关键词: Kolmogorov operators;    Multipolar potentials;    Weighted Hardy inequalities;    Optimal constant;   

DOI  :  10.1016/j.jmaa.2018.03.059

来源: Elsevier

【 摘 要 】

In this paper our main results are the multipolar weighted Hardy inequality c Sigma(n)(i=1) integral phi(2)/vertical bar x-a(i)vertical bar(2) d mu <= integral(RN) vertical bar del phi vertical bar(2)d mu+K integral(RN) phi(2)d mu, c <= c(o), where the functions phi belong to a weighted Sobolev space H-mu(1), and the proof of the optimality of the constant c(o) = c(o)(N) := (N-2/2)(2). The Gaussian probability measure d mu is the unique invariant measure for Ornstein-Uhlenbeck type operators. This estimate allows us to get necessary and sufficient conditions for the existence of positive solutions to a parabolic problem corresponding to the Kolmogorov operators defined on smooth functions and perturbed by a multipolar inverse square potential Lu+Vu = (Delta u+del mu/mu del u) + Sigma(n)(i=1) c/vertical bar x-a(i)vertical bar(2)u, x is an element of R-N, c > 0, a(1),..., a(n) is an element of R-N. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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