Calculus of Variations and Geometric Measure Theory

W. Borrelli - S. J. N. Mosconi - M. Squassina

Uniqueness of the critical point for solutions to some p-Laplace equations in the plane

created by borrelli on 01 Feb 2022
modified on 14 Dec 2023


Published Paper

Inserted: 1 feb 2022
Last Updated: 14 dec 2023

Journal: Rendiconti Lincei - Matematica e Applicazioni
Pages: 20
Year: 2022
Doi: 10.4171/RLM/997

ArXiv: 2201.12788 PDF

To appear on a special issue dedicated to Antonio Ambrosetti.


We prove that quasi-concave positive solutions to a class of quasi-linear elliptic equations driven by the p-Laplacian in convex bounded domains of the plane have only one critical point. As a consequence, we obtain strict concavity results for suitable transformations of these solutions.