We prove optimal regularity for solutions to the obstacle problem for a class of second order differential operators of Kolmogorov type. We treat smooth obstacles as well as non-smooth obstacles. All our proofs follow the same line of thought and are based on blow-ups, compactness, barriers and arguments by contradiction. This problem arises in nancial mathematics, when considering path-dependent derivative contracts with the early exercise feature.
@article{2230,
title = {Risultati di regolarit\`a per il problema dell'ostacolo relativo ad equazioni di Kolmogorov degeneri},
journal = {Bruno Pini Mathematical Analysis Seminar},
year = {2010},
doi = {10.6092/issn.2240-2829/2230},
language = {IT},
url = {http://dml.mathdoc.fr/item/2230}
}
Polidoro, Sergio. Risultati di regolarità per il problema dell'ostacolo relativo ad equazioni di Kolmogorov degeneri. Bruno Pini Mathematical Analysis Seminar, (2010), . doi : 10.6092/issn.2240-2829/2230. http://gdmltest.u-ga.fr/item/2230/