We consider a class of ultraparabolic differential equations that satisfy the Hoermander'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.
C. Cinti, A. Pascucci, S. Polidoro (2008). Pointwise estimates for solutions to a class of non-homogeneous Kolmogorov equations. MATHEMATISCHE ANNALEN, 340-2, 237-264 [10.1007/s00208-007-0147-6].
Pointwise estimates for solutions to a class of non-homogeneous Kolmogorov equations
PASCUCCI, ANDREA;
2008
Abstract
We consider a class of ultraparabolic differential equations that satisfy the Hoermander'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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.