Trudinger-Moser type inequalities for the Hessian equation with logarithmic weights
Analysis of PDEs
2025-04-15 v1
Abstract
We establish sharp Trudinger-Moser inequalities with logarithmic weights for the -Hessian equation and investigate the existence of maximizers. Our analysis extends the classical results of Tian and Wang to -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.
Cite
@article{arxiv.2504.09295,
title = {Trudinger-Moser type inequalities for the Hessian equation with logarithmic weights},
author = {João Marcos do Ó and José Francisco de Oliveira and Raoní Cabral Ponciano},
journal= {arXiv preprint arXiv:2504.09295},
year = {2025}
}