Techniques of Symmetrization and Mass Comparison for Nonlinear Parabolic and Elliptic Equations

What is it about?

We consider the solutions to various nonlinear parabolic equations and their elliptic counterparts and prove comparison results based on two main tools, symmetrization and mass concentration comparison. The work focuses on equations like the porous medium equation, the filtration equation and the p-Laplacian equation and includes of course the classical heat equation and the Laplace equation. The results will be used in a subsequent works in combination with a detailed knowledge of special solutions to obtain sharp a priori bounds and decay estimates for wide classes of solutions of those equations.

Featured Image

Why is it important?

Symmetrization reduces obtaining estimates for complex problems and data to easier ones where the calculations can be performed. The conclusions apply to the related more complex problems giving precious information. The present technique works well for nonlinear degenerate problems.

Perspectives