Abstract
We consider a class of ultraparabolic differential equations that satisfy the Hörmander’s hypoellipticity condition and we prove that the weak solutions to the equation with measurable coefficients are locally bounded functions. The method extends the Moser’s iteration procedure and has previously been employed in the case of operators verifying a further homogeneity assumption. Here we remove that assumption by proving some potential estimates and some ad hoc Sobolev type inequalities for solutions.
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Cinti, C., Pascucci, A. & Polidoro, S. Pointwise estimates for a class of non-homogeneous Kolmogorov equations. Math. Ann. 340, 237–264 (2008). https://doi.org/10.1007/s00208-007-0147-6
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DOI: https://doi.org/10.1007/s00208-007-0147-6