In this paper our main results are the multipolar weighted Hardy inequality for functions belonging to weighted Sobolev spaces and the proof of the optimality of the constant in the estimate. The Gaussian probablity measure 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.
Weighted Hardy inequalities and Ornstein-Uhlenbeck type operators perturbed by multipolar inverse square potentials
CANALE, Anna;
2018-01-01
Abstract
In this paper our main results are the multipolar weighted Hardy inequality for functions belonging to weighted Sobolev spaces and the proof of the optimality of the constant in the estimate. The Gaussian probablity measure 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.File in questo prodotto:
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