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The Second Hessian Type Equation on Almost Hermitian Manifolds
In this paper, we derive the second order estimate to the 2nd Hessian type equation on a compact almost Hermitian manifold.
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Hölder continuity for solutions of the complex Hessian type equation
In this paper we prove the Hölder continuity for the Hessian equation on a m -hyperconvex domain of m -subharmonic type k . As an application we prove...
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Existence of Positive Solutions for a Singular Hessian Equation with a Negative Augmented Term
In this paper, we focus on the existence of positive solutions for a singular Hessian equation with a negative augmented term. By finding more...
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Continuous Solutions for Degenerate Complex Hessian Equation
Let ( X , ω ) be an n -dimensional compact Kähler manifold and fix an integer m such that 1 ≤ m ≤ n . Let μ be a finite Borel measure on X satisfying the...
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Serrin-Type Overdetermined Problems for Hessian Quotient Equations and Hessian Quotient Curvature Equations
We consider overdetermined problems for Hessian quotient equations and Hessian quotient curvature equations, which are fully nonlinear elliptic...
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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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Hessian Equations of Krylov Type on Kähler Manifolds
In this paper, we consider a Hessian equation with its structure as a combination of elementary symmetric functions on closed Kähler manifolds. We...
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Existence and multiplicity of radially symmetric k-admissible solutions for a k-Hessian equation
In this paper, we show that the radially symmetric k -admissible solutions set of a k -Hessian equation Dirichlet problem with homogeneous boundary...
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Quasi-Newton Single-Phase Stability Testing without Explicit Hessian Calculation
AbstractA robust algorithm (solver) for testing the single-phase stability of a multicomponent fluid under isochoric-isobaric conditions is...
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On the Hessian-cscK equations
In this paper, we propose a coupled system of complex Hessian equations which generalizes the equation for constant scalar curvature Kähler (cscK)...
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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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Boundary Regularity for k-Hessian Equations
In this paper we focus on the boundary regularity for a class of k -Hessian equations which can be degenerate and (or) singular on the boundary of 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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The weak solutions to complex Hessian equations
In this paper, we shall study existence of weak solutions to complex Hessian equations on compact Hermitian manifolds. With appropriate assumptions,...
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Complex Hessian-Type Equations in the Weighted m-Subharmonic Class
We study the existence of a solution to a general type of complex Hessian equation on some Cegrell classes. For a given measure μ defined on an m -hype...
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Curvature estimates for a class of Hessian quotient type curvature equations
In this paper, we are concerned with the hypersurface that can be locally represented as a graph and satisfies a class of Hessian quotient type...