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arXiv · 2004.02712

Extremal functions for a supercritical k-Hessian inequality of Sobolev-type

José Francisco de Oliveira·Pedro Ubilla
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Abstract

Our main purpose in this paper is to investigate a supercritical Sobolev-type inequality for the $k$-Hessian operator acting on $\Phi^{k}_{0,\mathrm{rad}}(B)$, the space of radially symmetric $k$-admissible functions on the unit ball $B\subset\mathbb{R}^{N}$. We also prove both the existence of admissible extremal functions for the associated variational problem and the solvability of a related $k$-Hessian equation with supercritical growth.

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José Francisco de Oliveira, Pedro Ubilla. 2020-04-06. Extremal functions for a supercritical k-Hessian inequality of Sobolev-type. https://doi.org/10.1016/j.nonrwa.2021.103314

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