# Seminario di Equazioni Differenziali e Applicazioni: Comparisons and improved inequalities for semilinear elliptic equations

## Venerdì 30 Ottobre 2015, ore 11:30 - Aula 2AB40 - Francois Hamel

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI

Venerdì 30 Ottobre 2015 alle ore 11:30 in Aula 2AB40, Francois Hamel (Université d'Aix-Marseille) terrà un seminario dal titolo "Comparisons and improved inequalities for semilinear elliptic equations".

Abstract
I will talk about pointwise comparison results between the solutions of some second-order semilinear elliptic equations in a domain of $R^n$ and the solutions of some radially symmetric equations in the equimeasurable ball. The coefficients of the symmetrized equations in the ball satisfy similar constraints as the original ones in the original domain. I will consider both the case of equations with linear growth in the gradient and the case of equations with at most quadratic growth in the gradient. Some improved quantified comparisons when the original domain is not a ball will also be discussed. The method is based on a symmetrization of the second-order terms. The talk will be based on a joint work with Emmanuel Russ.

Rif. Int. M. Bardi, C. Marchi, L. Rossi