Pointwise estimates for degenerate Kolmogorov equations with Lp-source term.

The aim of this paper is to establish new pointwise regularity results for solutions to degenerate second-order partial differential equations with a Kolmogorov-type operator of the form L : = ∑ i , j = 1 m ∂ x i x j 2 + ∑ i , j = 1 N b ij x j ∂ x i - ∂ t , <graphic href="28_2022_763_Article_Equ79.gif"></graphic> where (x , t) ∈ R N + 1 , 1 ≤ m ≤ N and the matrix B : = (b ij) i , j = 1 , … , N has real constant entries. In particular, we show that if the modulus of L p -mean oscillation of L u at the origin is Dini, then the origin is a Lebesgue point of continuity in L p average for the second-order derivatives ∂ x i x j 2 u , i , j = 1 , … , m , and the Lie derivative ∑ i , j = 1 N b ij x j ∂ x i - ∂ t u . Moreover, we are able to provide a Taylor-type expansion up to second order with an estimate of the rest in L p norm. The proof is based on decay estimates, which we achieve by contradiction, blow-up and compactness results. [ABSTRACT FROM AUTHOR]