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The Exterior Problem of Parabolic Hessian Quotient Equations
MathematicsIn this paper, we investigate the exterior problem of parabolic Hessian quotient equations. By utilizing Perron’s method, we establish the existence of viscosity solutions that exhibit generalized asymptotic behavior at infinity.
Huawei Zhao, Limei Dai
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The Dirichlet Problem of Hessian Equation in Exterior Domains
Mathematics, 2020 In this paper, we will obtain the existence of viscosity solutions to the exterior Dirichlet problem for Hessian equations with prescribed asymptotic behavior at infinity by the Perron’s method. This extends the Ju–Bao results on Monge–Ampère equations
Hongfei Li, Limei Dai
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Local solvability of the k-Hessian equations [PDF]
Science China Mathematics, 2016 International audienceWe give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ k [u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be (k + 1)-convex ...
Xu, Chao-Jiang +3 more
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, 2009 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.
Wang, Xu-Jia +6 more
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We survey quadratic Hessian equations: definition, background, rigidity of entire solutions, regularity of viscosity solutions, a priori Hessian estimates, and open ...
Yuan, Yu
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Hessian equations and symmetrization
, 2005 In this paper we state some comparison results for solutions to Hessian type equations in dimension $n \ge 2$. These results involve convenient rearrangements of solutions that preserve suitable cross-sectional measures of their level ...
TROMBETTI, CRISTINA +3 more
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Regularity of degenerate Hessian equations [PDF]
Calculus of Variations and Partial Differential Equations, 2019 25 ...
Dinew, Sławomir +2 more
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Quasiconvex Functions and Hessian Equations [PDF]
Archive for Rational Mechanics and Analysis, 2003 Let \(S^{n\times n}\) denote the set of symmetric matrices. A continuous function \(f:S^{n\times n}\rightarrow\mathbb{R}\) is said to be quasiconvex (according to \textit{C. B. Morrey jun.} [Pac. J. Math. 2, 25--53 (1952; Zbl 0046.10803)]) if for any \(A\in S^{n\times n}\) and any smooth compactly supported function \(\varphi:\Omega\rightarrow\mathbb{R}
Faraco, Daniel, Zhong, Xiao
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Generalised solutions of Hessian equations [PDF]
Bulletin of the Australian Mathematical Society, 1997 We introduce a definition of generalised solutions of the Hessian equation Sm(D2u) = f in a convex set ω ⊂ ℝn, where Sm(D2u) denotes the m-th symmetric function of the eigenvalues of D2u, f ∈ Lp(ω), p ≥ 1, and m ∈ {1, …, n}. Such a definition is given in the class of semi-convex functions, and it extends the definition of convex generalised solutions ...
COLESANTI, ANDREA, SALANI, PAOLO
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