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Weighted Hardy inequalities and Ornstein-Uhlenbeck type operators perturbed by multipolar inverse square potentials (1708.00702v1)
Published 2 Aug 2017 in math.AP
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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