MAXIMUM AND ANTIMAXIMUM PRINCIPLES FOR THE p-LAPLACIAN WITH WEIGHTED STEKLOV BOUNDARY CONDITIONS - Archive ouverte HAL Access content directly
Journal Articles Electronic Journal of Differential Equations Year : 2020

MAXIMUM AND ANTIMAXIMUM PRINCIPLES FOR THE p-LAPLACIAN WITH WEIGHTED STEKLOV BOUNDARY CONDITIONS

Abstract

We study the maximum and antimaximum principles for the p-Laplacian operator under Steklov boundary conditions with an indefinite weight −∆pu + |u| p−2 u = 0 in Ω, |∇u| p−2 ∂u ∂ν = λm(x)|u| p−2 u + h(x) on ∂Ω, where Ω is a smooth bounded domain of R N , N > 1. After reviewing some elementary properties of the principal eigenvalues of the p-Laplacian under Steklov boundary conditions with an indefinite weight, we investigate the maximum and antimaximum principles for this problem. Also we give a characterization for the interval of the validity of the uniform antimaximum principle. 2010 Mathematics Subject Classification. 35J70. Key words and phrases. p-Laplacian; Steklov boundary conditions: indefinite weight; maximum and antimaximum principles.
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Dates and versions

hal-04121139 , version 1 (07-06-2023)

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  • HAL Id : hal-04121139 , version 1

Cite

Mabel Cuesta, Liamidi Leadi, Pascaline Nshimirimana. MAXIMUM AND ANTIMAXIMUM PRINCIPLES FOR THE p-LAPLACIAN WITH WEIGHTED STEKLOV BOUNDARY CONDITIONS. Electronic Journal of Differential Equations, 2020, 2020 (21), pp.1-17. ⟨hal-04121139⟩
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