Abstract
We establish a supercritical Trudinger–Moser type inequality for the k-Hessian operator on the space of the k-admissible radially symmetric functions \(\Phi ^{k}_{0,\textrm{rad}}(B)\), where B is the unit ball in \({\mathbb {R}}^{N}\). We also prove the existence of extremal functions for this new supercritical inequality.
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Acknowledgements
The authors would like to thank the anonymous referee for valuable suggestions that improved the quality of the paper.
Funding
J.F. de Oliveira acknowledges partial support from National Council for Scientific and Technological Development (CNPq) Grant Number 309491/2021-5; J.M. do Ó acknowledges partial support from National Council for Scientific and Technological Development (CNPq) through Grants 312340/2021-4, 409764/2023-0, 443594/2023-6, Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES) CAPES MATH AMSUD Grant 88887.878894/2023-00 and Paraíba State Research Foundation (FAPESQ), Grant No. 3034/2021; P. Ubilla acknowledges partial support from National Fund for Scientific and Technological Development FONDECYT 1220675.
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de Oliveira, J.F., do Ó, J.M. & Ubilla, P. On a supercritical k-Hessian inequality of Trudinger–Moser type and extremal functions. Annali di Matematica (2024). https://doi.org/10.1007/s10231-024-01455-x
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DOI: https://doi.org/10.1007/s10231-024-01455-x