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Extremal functions for a supercritical k-Hessian inequality of Sobolev-type
- Publication Year :
- 2020
-
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.
- Subjects :
- Mathematics - Analysis of PDEs
Mathematics - Functional Analysis
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2004.02712
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.nonrwa.2021.103314