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arXiv · 2505.03231

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

Rongxun He·Genggeng Huang
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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.

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Rongxun He, Genggeng Huang. 2025-05-06. Weighted Eigenvalue Problem for a Class of Singular/Degenerate $k$-Hessian Equations. https://arxiv.org/abs/2505.03231

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