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arXiv · 2505.03245

On the Hessian Hardy-Sobolev Inequality and Related Variational Problems

Rongxun He·Wei Ke
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Abstract

In this paper, we first prove the Hardy-Sobolev inequality for the Hessian integral by means of a descent gradient flow of certain Hessian functionals. As an application, we study the existence and regularity results of solutions to related variational problems. Our results extend the variational theory of the Hessian equation in \cite{CW01variational}.

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Rongxun He, Wei Ke. 2025-05-06. On the Hessian Hardy-Sobolev Inequality and Related Variational Problems. https://arxiv.org/abs/2505.03245

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