Results 21 to 30 of about 1,227,664 (287)
The Neumann Problem for Hessian Equations [PDF]
Communications in Mathematical Physics, 2019 25 ...
Xinan Ma, Guohuan Qiu
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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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Three-dimensional large-scale aerodynamic shape optimization based on shape calculus [PDF]
, 2013 Large-scale three-dimensional aerodynamic shape optimization based on the compressible Euler equations is considered. Shape calculus is used to derive an exact surface formulation of the gradients, enabling the computation of shape gradient information ...
Schmidt, Stephan +4 more
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G˚arding Cones and Bellman Equations in the Theory of Hessian Operators and Equations
Современная математика: Фундаментальные направления, 2017 In this work, we continue investigation of algebraic properties of G˚arding cones in the space of symmetric matrices. Based on this theory, we propose a new approach to study of fully nonlinear differential operators and second-order partial differential ...
N M Ivochkina, N V Filimonenkova
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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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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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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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On optimal solution error covariances in variational data assimilation problems [PDF]
, 2010 The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find unknown parameters such as distributed model coefficients or boundary conditions. The equation for the optimal solution error
Le Dimet, F.X. +3 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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Domain wall equations, Hessian of superpotential, and Bogomol'nyi bounds
Nuclear Physics B, 2016 An important question concerning the classical solutions of the equations of motion arising in quantum field theories at the BPS critical coupling is whether all finite-energy solutions are necessarily BPS.
Shouxin Chen, Yisong Yang
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