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

We prove L-loc(infinity) estimates for positive solutions to the following degenerate second order partial differential equation of Kolmogorov type with measurable coefficients of the form Sigma(m0)(i,j=1) partial derivative(xi) (a(ij)(x, t)partial derivative(xj) u(x, t) + Sigma(N)(i,j=1)b(ij)x(j)partial derivative(xj)u(x, t) - partial derivative(t) u(x, t) + Sigma(m0)(i=1) b(i)(x, t)partial derivative(i) u(x, t) - Sigma(m0)(i=1) partial derivative x(i)(a(i)(x, t)u(x, t)) + c(x, t)u(x, t) = 0 where (x, t) (x(1),... , x(N), t) = z is a point of R-N(+1), and 1 <= m(0) <= N. (a(ij)) is a uniformly positive symmetric matrix with bounded measurable coefficients, (b(ij)) 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. (C) 2019 Elsevier Ltd. All rights reserved.