Moser's estimates for degenerate Kolmogorov equations with non-negative divergence lower order coefficients

We prove Lloc ∞ estimates for positive solutions to the following degenerate second order partial differential equation of Kolmogorov type with measurable coefficients of the form ∑i,j=1m0∂xiaij(x,t)∂xju(x,t)+∑i,j=1Nbijxj∂xiu(x,t)−∂tu(x,t)++∑i=1m0bi(x,t)∂iu(x,t)−∑i=1m0∂xiai(x,t)u(x,t)+c(x,t)u(x,t)=0 where (x,t)=(x1,…,xN,t)=z is a point of RN+1, and 1≤m0≤N. (aij) is a uniformly positive symmetric matrix with bounded measurable coefficients, (bij) is a constant matrix. We apply the Moser's iteration method to prove the local boundedness of the solution u under minimal integrability assumption on the coefficients. © 2019 Elsevier Ltd