ABSTRACT
We give general conditions to state the weighted Hardy inequality
with respect to a probability measure . Moreover, the optimality of the constant
is given. The inequality is related to the following Kolmogorov equation perturbed by a singular potential
for which the existence of positive solutions to the corresponding parabolic problem can be investigated. The hypotheses on allow the drift term to be of type
with
.
Acknowledgements
The authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilitá e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).
Notes
No potential conflict of interest was reported by the authors.