Geodesic
G\aa rding cones and Bellman equations in the theory of Hessian operators and equations
Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 63 (2017) no. 4, pp. 615-626

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In this work, we continue investigation of algebraic properties of Gårding 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 equations. We prove new-type comparison theorems for evolution Hessian operators and establish a relation between Hessian and Bellman equations. 
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     author = {N. M. Ivochkina and N. V. Filimonenkova},
     title = {G\aa rding cones and {Bellman} equations in the theory of {Hessian} operators and equations},
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N. M. Ivochkina; N. V. Filimonenkova. G\aa rding cones and Bellman equations in the theory of Hessian operators and equations. Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 63 (2017) no. 4, pp. 615-626. http://geodesic.mathdoc.fr/item/CMFD_2017_63_4_a5/