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H\"older regularity for weak solutions of H\"ormander type operators

G. CittiM. MandrediniY. Sire
Dec 2022
摘要
Motivated by recent results on the (possibly conditional) regularity fortime-dependent hypoelliptic equations, we prove a parabolic version of thePoincar\'e inequality, and as a consequence, we deduce a version of theclassical Moser iteration technique using in a crucial way the geometry of theequation. The point of this contribution is to emphasize that one can use the{\sl elliptic} version of the Moser argument at the price of the lack ofuniformity, even in the {\sl parabolic } setting. This is nevertheless enoughto deduce H\"older regularity of weak solutions. The proof is elementary andunifies in a natural way several results in the literature on Kolmogorovequations, subelliptic ones and some of their variations.
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