Title

Weighted Hardy's inequality and the Kolmogorov equation perturbed by an inverse-square potential

Abstract

In this article, we give necessary and sufficient conditions for the existence of a weak solution of a Kolmogorov equation perturbed by an inverse-square potential. More precisely, using a weighted Hardy's inequality with respect to an invariant measure μ, we show the existence of the semigroup solution of the parabolic problem corresponding to a generalized Ornstein-Uhlenbeck operator perturbed by an inverse-square potential in L 2(ℝ N, μ). In the case of the classical Ornstein-Uhlenbeck operator we obtain nonexistence of positive exponentially bounded solutions of the parabolic problem if the coefficient of the inverse-square function is too large. © 2012 Copyright Taylor and Francis Group, LLC.

Publication Title

Applicable Analysis

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