Least energy solutions for affine $p$-Laplace equations involving subcritical and critical nonlinearities

Edir Junior Ferreira Leite; Marcos Montenegro

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arXiv · 2202.07030

Least energy solutions for affine $p$-Laplace equations involving subcritical and critical nonlinearities

Edir Junior Ferreira Leite·Marcos Montenegro

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Abstract

The paper is concerned with Lane-Emden and Brezis-Nirenberg problems involving the affine $p$-laplace nonlocal operator $\Delta_p^{\cal A}$, which has been introduced in \cite{HJM5} driven by the affine $L^p$ energy ${\cal E}_{p,\Omega}$ from convex geometry due to Lutwak, Yang and Zhang \cite{LYZ2}. We are particularly interested in the existence and nonexistence of positive $C^1$ solutions of least energy type. Part of the main difficulties are caused by the absence of convexity of ${\cal E}_{p,\Omega}$ and by the comparison ${\cal E}_{p,\Omega}(u) \leq \Vert u \Vert_{W^{1,p}_0(\Omega)}$ generally strict.

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Edir Junior Ferreira Leite, Marcos Montenegro. 2022-02-14. Least energy solutions for affine $p$-Laplace equations involving subcritical and critical nonlinearities. https://arxiv.org/abs/2202.07030

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