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

2022/02/14 by Leite, Edir Junior Ferreira, Montenegro, Marcos
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.07030

Abstract

The paper is concerned with Lane-Emden and Brezis-Nirenberg problems involving the affine p-laplace nonlocal operator Δ_p^{\cal A}, which has been introduced in \citeHJM5 driven by the affine L^p energy \cal E_p,Ω from convex geometry due to Lutwak, Yang and Zhang \citeLYZ2. We are particularly interested in the existence and nonexistence of positive C¹ solutions of least energy type. Part of the main difficulties are caused by the absence of convexity of \cal E_p,Ω and by the comparison \cal E_p,Ω(u) ≤ \Vert u \Vert_W^1,p0(Ω) generally strict.

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