Results 81 to 90 of about 5,752 (197)

Quadratic Hessian Equation

We survey quadratic Hessian equations: definition, background, rigidity of entire solutions, regularity of viscosity solutions, a priori Hessian estimates, and open problems.
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Eigenvalue problems for a k-Hessian-type equation

Nonlinear Analysis
In this work, we focus on the eigenvalue problem for a class of k-Hessian-type equations. Under some suitable assumptions, we first determine the intervals of the parameter for the existence of nontrivial radial solutions.
Zedong Yang, Zhanbing Bai
doaj   +1 more source

Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications

Journal of Function Spaces, 2018
We shall establish the global bifurcation results from the trivial solutions axis or from infinity for the Monge-Ampère equations: det(D2u)=λm(x)-uN+m(x)f1(x,-u,-u′,λ)+f2(x,-u,-u′,λ), in B, u(x)=0, on ∂B, where D2u=(∂2u/∂xi∂xj) is the Hessian matrix of u,
Wenguo Shen
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Complex Hessian Equation on Kähler Manifold [PDF]

International Mathematics Research Notices, 2009
12 ...
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The exterior Dirichlet problem for Hessian quotient equations

, 2012
In this paper, using a reverse MacLaurin inequality, we established the existence theorem of the exterior Dirichlet problem for Hessian quotient equations with a stronger asymptotic behavior at infinity. When k≤(n+1)/2, we improve the result in [L.M. Dai,
Li, Haigang, Dai, Limei
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Comparison results for Hessian equations via symmetrization

, 2007
In this paper, using symmetrization techniques, we prove comparison results for solutions to Hessian equations with homogeneous Dirichlet boundary conditions.
TROMBETTI, CRISTINA, BRANDOLINI, BARBARA
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A viscosity approach to the Dirichlet problem for degenerate complex Hessian-type equations

, 2018
29 pagesInternational audienceA viscosity approach is introduced for the Dirichlet problem associated to complex Hessian type equations on domains in $\C^n$.
Dinew, Sławomir, Do, Hoang-Son, Tô, Tat Dat, Dinew, Slawomir   +3 more
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Approximating large-scale Hessian matrices using secant equations [PDF]

Large-scale optimization algorithms frequently require sparse Hessian matrices that are not readily available. Existing methods for approximating large sparse Hessian matrices either do not impose sparsity or are computationally prohibitive. To try and
Fowkes, Jaroslav M., Scott, Jennifer A., Gould, Nicholas I. M.   +2 more
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Interior Estimates for Generalized Forchheimer Flows of Slightly Compressible Fluids

Advanced Nonlinear Studies, 2017
The generalized Forchheimer flows are studied for slightly compressible fluids in porous media with time-dependent Dirichlet boundary data for the pressure. No restrictions are imposed on the degree of the Forchheimer polynomial. We derive, for all time,
Hoang Luan T., Kieu Thinh T.
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HESSIAN EQUATIONS WITH INFINITE DIRICHLET BOUNDARY VALUE

, 2014
In this paper, we will show the existence and non-existence of Hessian equations with infinite Dirichlet boundary value conditions. Kewwords Hessian equation, k-convex solution, singular boundary value, existence/nonexistence, viscous solution ...
Huaiyu Jian, Xiuqing Chen
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