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Necessary and sufficient conditions on global solvability for the p-k-Hessian inequalities

Part of: Partial differential equations Elliptic equations and systems

Published online by Cambridge University Press:  17 January 2022

Jiguang Bao  and
Qiaoli Feng
Jiguang Bao
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China e-mail: jgbao@bnu.edu.cn
Qiaoli Feng*
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China e-mail: jgbao@bnu.edu.cn
*
e-mail: 201921130018@mail.bnu.edu.cn
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Abstract

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.

Keywords

p-k-Hessian inequalitysolvabilityoptimal regularityKeller–Osserman condition

MSC classification

Primary: 35B65: Smoothness and regularity of solutions
Secondary: 35J60: Nonlinear elliptic equations
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 4 , December 2022 , pp. 1004 - 1019
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Copyright
© Canadian Mathematical Society, 2022

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Footnotes

The authors are supported partially by the National Natural Science Foundation of China (11871102 and 11631002).

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