Necessary and sufficient conditions on global solvability for the p-k-Hessian inequalities
Canadian mathematical bulletin, Tome 65 (2022) no. 4, pp. 1004-1019
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In this paper, we discuss the solvability of the p-k-Hessian inequality $\sigma _{k}^{\frac 1k} ( \lambda ( D_{i} (|Du|^{p-2}$$ D_{j}u ) ) ) \geq f(u)$ on the entire space $\mathbb {R}^{n}$ and provide a necessary and sufficient condition, which can be regarded as a generalized Keller–Osserman condition. Furthermore, we obtain the optimal regularity of solution.
Mots-clés :
p-k-Hessian inequality, solvability, optimal regularity, Keller–Osserman condition
Bao, Jiguang; Feng, Qiaoli. Necessary and sufficient conditions on global solvability for the p-k-Hessian inequalities. Canadian mathematical bulletin, Tome 65 (2022) no. 4, pp. 1004-1019. doi: 10.4153/S0008439522000066
@article{10_4153_S0008439522000066,
author = {Bao, Jiguang and Feng, Qiaoli},
title = {Necessary and sufficient conditions on global solvability for the {p-k-Hessian} inequalities},
journal = {Canadian mathematical bulletin},
pages = {1004--1019},
year = {2022},
volume = {65},
number = {4},
doi = {10.4153/S0008439522000066},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000066/}
}
TY - JOUR AU - Bao, Jiguang AU - Feng, Qiaoli TI - Necessary and sufficient conditions on global solvability for the p-k-Hessian inequalities JO - Canadian mathematical bulletin PY - 2022 SP - 1004 EP - 1019 VL - 65 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000066/ DO - 10.4153/S0008439522000066 ID - 10_4153_S0008439522000066 ER -
%0 Journal Article %A Bao, Jiguang %A Feng, Qiaoli %T Necessary and sufficient conditions on global solvability for the p-k-Hessian inequalities %J Canadian mathematical bulletin %D 2022 %P 1004-1019 %V 65 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000066/ %R 10.4153/S0008439522000066 %F 10_4153_S0008439522000066
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