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Curvature estimates for a class of Hessian type equations
In this paper, we establish the curvature estimates for a class of Hessian type equations. Some applications are also discussed.
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Regularity for a Class of Singular Complex Hessian Equations
In this paper, we study the regularity of the complex Hessian equation when the right hand has pole singularity. We show the Hölder continuity of the...
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A Hessian-Dependent Functional With Free Boundaries and Applications to Mean-Field Games
We study a Hessian-dependent functional driven by a fully nonlinear operator. The associated Euler-Lagrange equation is a fully nonlinear mean-field...
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Fast Convex Optimization via Differential Equation with Hessian-Driven Dam** and Tikhonov Regularization
In this paper, we consider a class of second-order ordinary differential equations with Hessian-driven dam** and Tikhonov regularization, which...
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On the hyperbolic nonlinear Schrödinger equations
Here, we consider here Hyperbolic Nonlinear Schrödinger Equations (HNLS) that occur as asymptotic models in the modulational regime when the Hessian...
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Existence of entire radial solutions to Hessian type system
In this paper, the Dirichlet problem of Hessian type system is studied. After converting the existence of an entire solution to the existence of a...
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Hessian Informed Mirror Descent
Inspired by the recent paper (L. Ying, Journal of Scientific Computing, 84, 1–14 (2020), we explore the relationship between the mirror descent and...
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Overdetermined problems for fully nonlinear equations with constant Dirichlet boundary conditions in space forms
We consider overdetermined problems for two classes of fully nonlinear equations with constant Dirichlet boundary conditions in a bounded domain in...
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Modification of the Confidence Bar Algorithm Based on Approximations of the Main Diagonal of the Hessian Matrix for Solving Optimal Control Problems
AbstractThe paper proposes an approach to the study of the standard optimal control problem based on the use of reduction to a finite-dimensional...
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Hessian discretisation method for fourth-order semi-linear elliptic equations: applications to the von Kármán and Navier–Stokes models
This paper deals with the Hessian discretisation method (HDM) for fourth-order semi-linear elliptic equations with a trilinear non-linearity. The HDM...
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Discrete Hessian Complexes in Three Dimensions
A family of conforming virtual element Hessian complexes on tetrahedral meshes are constructed based on decompositions of polynomial tensor spaces....
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Symmetry of solutions of minimal gradient graph equations on punctured space
In this paper, we study symmetry and existence of solutions of minimal gradient graph equations on punctured space ℝ n \ {0}, which include the...
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Gradient and Hessian Estimates for the Hermitian Monge–Ampère Equation
We substantially improve our previous gradient estimate for the Monge–Ampère equation on a compact Hermitian manifold. The improvements concern the...
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Hessian estimates for Lagrangian mean curvature equation
In this paper, we derive a priori interior Hessian estimates for the Lagrangian mean curvature equation if the Lagrangian phase is supercritical and...
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Hessian barrier algorithms for non-convex conic optimization
A key problem in mathematical imaging, signal processing and computational statistics is the minimization of non-convex objective functions that may...
