Anna Chiara Zagati: Sharp geometric estimates and asymptotic behaviour for solutions of Lane- Emden equation

Abstract.

We introduce the Lane-Emden equation for the p−Laplacian with the sub-homogeneous power on the right-hand side. Then we prove, throughout a comparison principle, a variety of results, as the uniqueness of solutions under minimal assumptions on the set, sharp pointwise two-sided estimates for positive olutions in convex sets and a “hierarchy” of sign-changing solutions of the equation. Finally we study the asymptotic behaviour for positive solutions, as p goes to ∞. The results presented in this talk are obtained in collaboration with Lorenzo Brasco (University of Ferrara) and Francesca Prinari (University of Pisa).