Principal eigenvalues for the weighted p-Laplacian and antimaximum principle in ℝ^N

2025/04/24 by Joseph, Anumol, Sarkar, Abhishek
#35A15 #35B40 #35J62 #35J92 #35P30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.17325

Abstract

We study the existence of principal eigenvalues and principal eigenfunctions for weighted eigenvalue problems of the form: - div ( L (x) |∇ u|^p-2 ∇ u ) = λK(x) |u|^p-2 u \hspace.1cm \mbox in \hspace.1cm ℝ^N , where λ∈ ℝ, p>1, K : ℝ^N → ℝ, L : ℝ^N → ℝ⁺ are locally integrable functions. The weight function K is allowed to change sign, provided it remains positive on a set of nonzero measure. We establish the existence, regularity, and asymptotic behavior of the principal eigenfunctions. We also prove local and global antimaximum principles for a perturbed version of the problem.

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