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

William Borrelli; Sunra Mosconi; Marco Squassina

doi:10.4171/RLM/997

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

William Borrelli, Sunra Mosconi, Marco Squassina

University of Catania

Risultato della ricerca: Contributo in rivista › Articolo in rivista

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.

Lingua originale	English
pagine (da-a)	61-88
Numero di pagine	28
Rivista	ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI
Volume	34
DOI	https://doi.org/10.4171/RLM/997
Stato di pubblicazione	Pubblicato - 2023

Keywords

Quasilinear problems
convexity of solutions
maximum principles

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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.",

keywords = "Quasilinear problems, convexity of solutions, maximum principles, Quasilinear problems, convexity of solutions, maximum principles",

author = "William Borrelli and Sunra Mosconi and Marco Squassina",

year = "2023",

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AU - Squassina, Marco

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AB - 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.

KW - Quasilinear problems

KW - convexity of solutions

KW - maximum principles

KW - Quasilinear problems

KW - convexity of solutions

KW - maximum principles

UR - http://hdl.handle.net/10807/269615

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JF - ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI

ER -

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

Abstract

Keywords

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