Estimates of Green functions and their applications for parabolic operators with singular potentials
Volume 95 / 2003
Colloquium Mathematicum 95 (2003), 267-283
MSC: 31B25, 35B05, 35K10.
DOI: 10.4064/cm95-2-10
Abstract
We prove global pointwise estimates for the Green function of a parabolic operator with potential in the parabolic Kato class on a $C^{1,1}$ cylindrical domain ${\mit \Omega }$. We apply these estimates to obtain a new and shorter proof of the Harnack inequality [16], and to study the boundary behavior of nonnegative solutions.
