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

William Borrelli; Sunra Mosconi; Marco Squassina

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arXiv · 2201.12788

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

William Borrelli·Sunra Mosconi·Marco Squassina

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Abstract

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.

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William Borrelli, Sunra Mosconi, Marco Squassina. 2022-01-30. Uniqueness of the critical point for solutions to some $p$-Laplace equations in the plane. https://arxiv.org/abs/2201.12788

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