Results 21 to 30 of about 5,752 (197)
Mathematische Zeitschrift, 2023 In this paper, we propose a coupled system of complex Hessian equations which generalizes the equation for constant scalar curvature Kähler (cscK) metrics. We show this system can be realized variationally as the Euler-Lagrange equation of a Hessian version of the Mabuchi K-energy in an infinite dimensional space of $k$-Hessian potentials, which can be
Guo, Bin, Smith, Kevin, Tong, Freid
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Asymptotic mean-value formulas for solutions of general second-order elliptic equations
Advanced Nonlinear Studies, 2022 We obtain asymptotic mean-value formulas for solutions of second-order elliptic equations. Our approach is very flexible and allows us to consider several families of operators obtained as an infimum, a supremum, or a combination of both infimum and ...
Blanc Pablo +3 more
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On the regularity of the complex Hessian equation [PDF]
Proceedings of the American Mathematical Society, 2022 This note aims to investigate the regularity of a solution to the Dirichlet problem for the complex Hessian equation, which has a density of the m m
Åhag, Per, Czyż, Rafał
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Unilateral Global Interval Bifurcation for the Hessian Equation and Its Applications
Discrete Dynamics in Nature and Society, 2020 In this paper, we establish a unilateral global bifurcation result from the interval for the k-Hessian equations with nondifferentiable nonlinearity. By applying the above result, we shall prove the existence of the principal half-eigenvalues for the ...
Wenguo Shen
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Hessian equations of Krylov type on compact Hermitian manifolds
Open Mathematics, 2022 In this article, we are concerned with the equations of Krylov type on compact Hermitian manifolds, which are in the form of the linear combinations of the elementary symmetric functions of a Hermitian matrix.
Zhou Jundong, Chu Yawei
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Entropy, 2020 A method is developed to complete an incomplete set of equations of state of a thermodynamic system. Once the complete set of equations is found, in order to verify the thermodynamic validity of a system, the Hessian and entropy methods are exposed.
Karen Arango-Reyes +1 more
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On a class of obstacle problem for Hessian equations on Riemannian manifolds
Journal of Inequalities and Applications, 2023 In this paper, we establish the a priori C 2 $C^{2}$ estimates for solutions of a class of obstacle problem for Hessian equations on Riemannian manifolds. Some applications are also discussed. The main contribution of this paper is the boundary estimates
Jinxuan Liu, Yong Wang
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A variational theory of the Hessian equation
Communications on Pure and Applied Mathematics, 2001 AbstractBy studying a negative gradient flow of certain Hessian functionals we establish the existence of critical points of the functionals and consequently the existence of ground states to a class of nonhomogenous Hessian equations. To achieve this we derive uniform, first‐ and second‐order a priori estimates for the elliptic and parabolic Hessian ...
Chou, Kai-Seng, Wang, Xu-Jia
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A short note on Harnack inequality for k-Hessian equations with nonlinear gradient terms [PDF]
Opuscula MathematicaIn this short note we study a Harnack inequality for \(k\)-Hessian equations that involve nonlinear lower-order terms which depend on the solution and its gradient.
Ahmed Mohammed, Giovanni Porru
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Regularity of degenerate k-Hessian equations on closed Hermitian manifolds
Advanced Nonlinear Studies, 2022 In this article, we are concerned with the existence of weak C1,1{C}^{1,1} solution of the kk-Hessian equation on a closed Hermitian manifold under the optimal assumption of the function in the right-hand side of the equation.
Zhang Dekai
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