Geometric character of domain and the Harnack inequality of solution of a singular parabolic equation

Year, pages: 2012, 721 - 734

The geometric character of domains of solutions of a singular parabolic equation with the Neumann boundary condition are discussed in this work. We prove a gradient estimate and a Harnack type inequality and then, show that the domains of the solutions are exactly columns in the space-time. Specially, the altitudes of the columns are calculated accurately.

Pan, J. 2012. Geometric character of domain and the Harnack inequality of solution of a singular parabolic equation. In Mathematica Slovaca, vol. 62, no.4, pp. 721-734. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0040-y

Pan, J. (2012). Geometric character of domain and the Harnack inequality of solution of a singular parabolic equation. Mathematica Slovaca, 62(4), 721-734. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0040-y