Results 31 to 40 of about 1,227,664 (287)

Isoperimetric inequalities for -Hessian equations

Advances in Nonlinear Analysis, 2012
We consider the homogeneous Dirichlet problem for a special -Hessian equation of sub-linear type in a -convex domain , . We study the comparison between the solution of this problem and the (radial) solution of the corresponding problem in a ball having ...
Mohammed Ahmed, Porru Giovanni, Safoui Abdessalam   +2 more
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A short note on Harnack inequality for k-Hessian equations with nonlinear gradient terms [PDF]

Opuscula Mathematica
In this short note we study a Harnack inequality for \(k\)-Hessian equations that involve nonlinear lower-order terms which depend on the solution and its gradient.
Ahmed Mohammed, Giovanni Porru
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Iterative methods for $k$-Hessian equations [PDF]

Methods and Applications of Analysis, 2018
On a domain of the n-dimensional Euclidean space, and for an integer k=1,...,n, the k-Hessian equations are fully nonlinear elliptic equations for k >1 and consist of the Poisson equation for k=1 and the Monge-Ampere equation for k=n. We analyze for smooth non degenerate solutions a 9-point finite difference scheme. We prove that the discrete scheme
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Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations

Boundary Value Problems, 2022
In this paper, we consider the exterior Dirichlet problem of Hessian equations σ k ( λ ( D 2 u ) ) = g ( x ) $\sigma _{k}(\lambda (D^{2}u))=g(x)$ with g being a perturbation of a general positive function at infinity. By estimating the eigenvalues of the
Limei Dai, Hongfei Li
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Asymptotic behavior of solutions of fully nonlinear equations over exterior domains

Comptes Rendus. Mathématique, 2021
In this paper, we consider the asymptotic behavior at infinity of solutions of a class of fully nonlinear elliptic equations $F(D^2u)=f(x)$ over exterior domains, where the Hessian matrix $(D^2u)$ tends to some symmetric positive definite matrix at ...
Jia, Xiaobiao
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A priori estimates for complex Hessian equations [PDF]

Analysis & PDE, 2014
We prove some $L^{\infty}$ a priori estimates as well as existence and stability theorems for the weak solutions of the complex Hessian equations in domains of $C^n$ and on compact Kähler manifolds. We also show optimal $L^p$ integrability for m-subharmonic functions with compact singularities, thus partially confirming a conjecture of Blocki.
Dinew, Sławomir, Kołodziej, Sławomir
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Regularity of degenerate k-Hessian equations on closed Hermitian manifolds

Advanced Nonlinear Studies, 2022
In this article, we are concerned with the existence of weak C1,1{C}^{1,1} solution of the kk-Hessian equation on a closed Hermitian manifold under the optimal assumption of the function in the right-hand side of the equation.
Zhang Dekai
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Stability of the equator map for the Hessian energy [PDF]

Proceedings of the American Mathematical Society, 2007
Summary: We show that the equator map is a minimizer of the Hessian energy \( H(u)=\int _{\Omega } |\Delta u|^{2}\,dx\) in \( H^{2}(\Omega ;S^{n})\) for \( n\geq 10\) and is unstable for \( 5\leq n\leq 9\).
Hong, M. C., Thompson, B.
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Serrin-type overdetermined problems for Hessian quotient equations

, 2022
We prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely Hessian quotient equations and Hessian quotient curvature equations. Our approach is based on establishing a Rellich-Pohozaev type identity for
Gao, Zhenghuan, Zhang, Dekai, Jia, Xiaohan   +2 more
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The weak solutions to complex Hessian equations [PDF]

, 2023
In this paper, we shall study existence of weak solutions to complex Hessian equations.
Sun, Wei
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