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arXiv · 2211.14817

Principal curves to fractional $m$-Laplacian systems and related maximum and comparison principles

Anderson Luis Albuquerque de Araujo·Edir Junior Ferreira Leite·Aldo Henrique de Souza Medeiros
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Abstract

In this paper we develop a comprehensive study on principal eigenvalues and both the (weak and strong) maximum and comparison principles related to an important class of nonlinear systems involving fractional $m$-Laplacian operators. Explicit lower bounds for principal eigenvalues of this system in terms of the diameter of $\Omega$ are also proved. As application, given $\lambda,\mu\geq 0$ we measure explicitly how small has to be $\text{diam}(\Omega)$ so that weak and strong maximum principles associated to this problem hold in $\Omega$.

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Anderson Luis Albuquerque de Araujo, Edir Junior Ferreira Leite, Aldo Henrique de Souza Medeiros. 2022-11-27. Principal curves to fractional $m$-Laplacian systems and related maximum and comparison principles. https://arxiv.org/abs/2211.14817

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