Estimates of Green functions and their applications for parabolic operators with singular potentials

Volume 95 / 2003

Lotfi Riahi 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.

Authors

  • Lotfi RiahiDepartment of Mathematics
    Faculty of Sciences of Tunis
    Campus Universitaire 1060
    Tunis, Tunisia
    e-mail

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