Necessary and sufficient conditions on global solvability for the <i>p</i>-<i>k</i>-Hessian inequalities

2022/01/17 by Jiguang Bao, Qiaoli Feng · 1 citation
Mathematics · Biochemistry, Genetics and Molecular Biology · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Dermatological and Skeletal Disorders

paper · doi:10.4153/s0008439522000066

Abstract

Abstract In this paper, we discuss the solvability of the p - k -Hessian inequality σ _k^{\frac 1k} ( λ ( D_i (|Du|^p-2 D_ju ) ) ) ≥ f(u) on the entire space \mathbb Rⁿ 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.

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• Entire solvability for a class of p-k-Hessian equations with gradient terms

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