Pointwise estimates for a class of non-homogeneous Kolmogorov equations

By C. Cinti, Andrea Pascucci, Sergio Polidoro. 2008

48 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f77d925a9d972529fdf7a82d0b4e0bf5bd600bca

Citations in the corpus

• A survey on the classical theory for Kolmogorov equation (2019, unknown): “The theory of Kolmogorov operators with measurable coefficients ai j is developed in the following papers: • Moser iteration: a first contribution is given by Polidoro and Pascucci (see [60]) for dilation invariant Kolmogorov operators with measurable coefficients; later on, Cinti, Pascucci and Poli”