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arXiv · 2603.25511

Uniform estimates and Brezis-Merle type inequalities for the $k$-Hessian equation

Jie Deng·Haibin Wang·Bin Zhou
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Abstract

In this paper, we prove a Brezis-Merle type inequality for $k$-convex functions vanishing on the boundary. As an application, we establish an Alexandrov-Bakelman-Pucci type estimate for the intermediate Hessian equation. Furthermore, we establish a concentration-compactness principle for the blow-up behavior of solutions to the mean field type $k$-Hessian equation.

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Jie Deng, Haibin Wang, Bin Zhou. 2026-03-26. Uniform estimates and Brezis-Merle type inequalities for the $k$-Hessian equation. https://arxiv.org/abs/2603.25511

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