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arXiv · 2504.09295

Trudinger-Moser type inequalities for the Hessian equation with logarithmic weights

João Marcos do Ó·José Francisco de Oliveira·Raoní Cabral Ponciano
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Abstract

We establish sharp Trudinger-Moser inequalities with logarithmic weights for the $k$-Hessian equation and investigate the existence of maximizers. Our analysis extends the classical results of Tian and Wang to $k$-admissible function spaces with logarithmic weights, providing a natural complement to the work of Calanchi and Ruf. Our approach relies on transforming the problem into a one-dimensional weighted Sobolev space, where we solve it using various techniques, including some radial lemmas and certain Hardy-type inequalities, which we establish in this paper, as well as a theorem due to Leckband.

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João Marcos do Ó, José Francisco de Oliveira, Raoní Cabral Ponciano. 2025-04-12. Trudinger-Moser type inequalities for the Hessian equation with logarithmic weights. https://doi.org/10.1016/j.jde.2026.114660

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