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Loss of regularity for Kolmogorov equations
(2012)The celebrated H ormander condition is a sucient (and nearly necessary) condition for a second-order linear Kolmogorov partial dierential equation (PDE) with smooth coecients to be hypoelliptic. As a consequence, the solutions of Kolmogorov PDEs are smooth at all positive times if the coecients of the PDE are smooth and satisfy H ormander's condition even if the initial function is only continuous but not dierentiable. First-order linear ...Report