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Moser–Trudinger Type Inequalities for the Hessian Equation
Journal of Functional Analysis, 2010 The k-Hessian equation for k⩾2 is a class of fully nonlinear partial differential equation of divergence form. A Sobolev type inequality for the k-Hessian equation was proved by the second author in 1994.
Xu-Jia Wang
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The Eigenvalue Problem of a Singular k-Hessian Equation
Applied Mathematics Letters, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xinguang Zhang, Yonghong Wu
exaly +3 more sources
Boundary Regularity for k-Hessian Equations
Acta Mathematica Sinica, English Series, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, You, Li, Meng Ni, Liu, Yan Nan
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Existence of k-Convex Solutions for the k-Hessian Equation
Mediterranean Journal of Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bai, Zhanbing, Yang, Zedong
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Viscosity solutions of the augmented K- Hessian equations
HPU2 Journal of Science: Natural Sciences and Technology, 2022In this paper, the Dirichlet problem for the augmented k – Hessian equations in the bounded domain with nonsmooth data will be investigated. We introduce the concept of (w,k) – convex function, show that all viscosity subsolutions and supersolutions of the considering Dirichlet problem are (w,k) – convex.
Van - Bang Tran +4 more
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Existence for a k-Hessian equation involving supercritical growth
Journal of Differential Equations, 2019The authors consider a supercritical Drichlet problem involving the \(k\)th Hessian operator and they prove the existence of a radial solution by using a minimax method without the Palais-Smale condition. It seems to be a good result.
José Francisco de Oliveira +2 more
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The Liouville theorem for k-Hessian equations in the half space
Calculus of Variations and Partial Differential EquationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jia, Xiaobiao, Ma, Shanshan
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Existence and uniqueness of nontrivial radial solutions for k-Hessian equations
Journal of Mathematical Analysis and Applications, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On aspects of radial solutions for a class of augmented k-Hessian equations
Journal of Fixed Point Theory and ApplicationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mi, Ling, Feng, Shu
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