Results 11 to 20 of about 13,144,199 (261)
A Gradient Type Term for the k-Hessian Equation [PDF]
The Journal of Geometric Analysis, 2023 In this paper, we propose a gradient type term for the $k$-Hessian equation that extends for $k>1$ the classical quadratic gradient term associated with the Laplace equation. We prove that such as gradient term is invariant by the Kazdan-Kramer change of variables.
Mykael Cardoso +2 more
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Local solvability of the k-Hessian equations [PDF]
Science China Mathematics, 2016 In this work, we study the existence of local solutions in $\mathbb{R}^{n}$ to $k$-Hessian equation,for which the nonhomogeneous term $f$ is permitted to change the sign or be non negative; if $f$ is $C^\infty,$ so is the local solution. We also give a classification for the second order polynomial solutions to the $k-$Hessian equation, it is the basis
Tian, Guji, Wang, Qi, Xu, Chao-Jiang
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, 2009 Abstract The k-Hessian is the k-trace, or the kth elementary symmetric polynomial of eigenvalues of the Hessian matrix. When k ≥ 2, the k-Hessian equation is a fully nonlinear partial differential equations. It is elliptic when restricted to k-admissible functions. In this paper we establish the existence and regularity of k-admissible solutions to the
Gursky, Matthew +5 more
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A quantitative result for the $k$-Hessian equation [PDF]
In this paper, we study a symmetrization that preserves the mixed volume of the sublevel sets of a convex function, under which, a Pólya-Szeg\H o type inequality holds. We refine this symmetrization to obtain a quantitative improvement of the Pólya-Szeg\H o inequality for the $k$-Hessian integral, and, with similar arguments, we show a quantitative ...
Masiello A. L., Salerno F.
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Eigenvalue problems for a k-Hessian-type equation
Nonlinear AnalysisIn this work, we focus on the eigenvalue problem for a class of k-Hessian-type equations. Under some suitable assumptions, we first determine the intervals of the parameter for the existence of nontrivial radial solutions.
Zedong Yang, Zhanbing Bai
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THE DIRICHLET PROBLEM OF THE HOMOGENEOUS k-HESSIAN EQUATION IN A PUNCTURED DOMAIN [PDF]
, 2023 In this paper, we consider the Dirichlet problem for the homogeneous $k$-Hessian equation with prescribed asymptotic behavior at $0\inΩ$ where $Ω$ is a $(k-1)$-convex bounded domain in the Euclidean space. The prescribed asymptotic behavior at $0$ of the solution is zero if $k>\frac{n}{2}$, it is $\log|x|+O(1)$ if $k=\frac{n}{2}$ and $-|x|^{\frac{2k-
Gao, Zhenghuan, Ma, Xi-Nan, Zhang, Dekai
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Complex Hessian Equations on Some Compact Kähler Manifolds [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 On a compact connected 2m-dimensional Kähler manifold with Kähler form ω, given a smooth function f:M→ℝ and an integer ...
Asma Jbilou
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Non-convexity of level sets for k-Hessian equations in convex ring
Mathematische ZeitschriftIn this paper we construct explicit examples that show the sublevel sets of the solution of a $k$-Hessian equation defined on a convex ring do not have to be convex.
Wang, Zhizhang, Xiao, Ling
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A characterization of semistable radial solutions of k-Hessian equations [PDF]
Journal of Mathematical Analysis and Applications, 2021 We characterize semistable radial solutions of the equation $S_k\left(D^2u\right)=g(u)\;\mbox{in } B_1$, where $B_1$ is the unit ball of $\mathbb{R}^n$, $D^2u$ is the Hessian matrix of $u,\,g$ is a positive $C^1$ nonlinearity and $S_k\left(D^2u\right)$ denotes the $k$-Hessian operator of $u$.
Miguel Angel Navarro Burgos +1 more
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The Dirichlet problem for the k-Hessian equation on a complex manifold
American Journal of Mathematics, 2022 We solve the Dirichlet problem for $k$-Hessian equations on compact complex manifolds with boundary, given the existence of a subsolution. Our method is based on a second order a priori estimate of the solution on the boundary with a particular gradient scale.
Collins, Tristan C., Picard, Sebastien
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