Comparison results for solutions of parabolic equations with a singular potential

Abstract

We consider the solution u of the Cauchy-Dirichlet problem for a class of linear parabolic equations in which the coefficient of the zero order term could have a singularity at the origin of the type 1/|x|^2 . We prove that u can be compared “in the sense of rearrangements” with the solution v of a problem whose data are radially symmetric with respect to the space variable.

Keywords

• Reaarngements
• Comparison results
• Schwarz symmetrization
• Parabolic equations