A comparison principle for the Lane-Emden equation and applications to geometric estimates – Anna Chiara Zagati (Università di Ferrara)

Venue

Aula Magna – Dipartimento di Matematica.

Abstract

We introduce a comparison principle for positive supersolutions and subsolutions to the Lane-Emden equation for the p−Laplacian. Then we apply such a comparison principle to obtain a variety of results, as “hierarchy” of solutions, sharp pointwise double-side estimates for positive solutions in convex sets, and a sharp geometric estimate on the generalized principal frequencies of convex sets, which provides a generalization of the so-called Hersch-Protter inequality. Link to attend remotely available at: https://seminarimap.wixsite.com/seminarimap/2021-2022/anna-chiara-zagati

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