We study the effect on the solutions of linear parabolic equations of Gaussian symmetrization. This kind of symmetrization, which transforms a domain into an half-space with the same Gaussian measure, is specifically useful when the domain is unbounded. The main tools we use are the properties of the weighted rearrangements and in particular the isoperimetric inequality with respect to Gaussian measure.
"Comparison results for linear parabolic equations in unbounded domains via Gaussian symmetrization." Differential Integral Equations 17 (3-4) 241 - 258, 2004. https://doi.org/10.57262/die/1356060433