Work

Weighted Eigenvalue Problem for a Class of Singular/Degenerate $k$-Hessian Equations

Year: 2025

Type: preprint

Abstract: In this paper, we study the existence and uniqueness of solutions to the weighted eigenvalue problem for $k$-Hessian equation. To achieve this, we establish the uniform a priori estimates for gradient and second derivatives of solutions to Hessian equation with weight $|x|^{2sk}$ on the right-hand-side. We also prove that the eigenfunction is a minimizer of the corresponding functional among all $k$-admissible functions vanishing on the boundary.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2505.03231

Authors: He, Rongxun, Huang, Genggeng

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4415248152

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