Results 11 to 20 of about 5,752 (197)

Local solvability of the k-Hessian equations [PDF]

Science China Mathematics, 2016
In this work, we study the existence of local solutions in $\mathbb{R}^{n}$ to $k$-Hessian equation,for which the nonhomogeneous term $f$ is permitted to change the sign or be non negative; if $f$ is $C^\infty,$ so is the local solution. We also give a classification for the second order polynomial solutions to the $k-$Hessian equation, it is the basis
Tian, Guji, Wang, Qi, Xu, Chao-Jiang
openaire   +6 more sources

The Dirichlet Problem of Hessian Equation in Exterior Domains

Mathematics, 2020
In this paper, we will obtain the existence of viscosity solutions to the exterior Dirichlet problem for Hessian equations with prescribed asymptotic behavior at infinity by the Perron’s method. This extends the Ju–Bao results on Monge–Ampère equations
Hongfei Li, Limei Dai
doaj   +2 more sources

The Exterior Problem of Parabolic Hessian Quotient Equations

Mathematics
In this paper, we investigate the exterior problem of parabolic Hessian quotient equations. By utilizing Perron’s method, we establish the existence of viscosity solutions that exhibit generalized asymptotic behavior at infinity.
Huawei Zhao, Limei Dai
doaj   +2 more sources

The Neumann Problem for Hessian Equations [PDF]

Communications in Mathematical Physics, 2019
25 ...
Xinan Ma, Guohuan Qiu
openaire   +4 more sources

Domain wall equations, Hessian of superpotential, and Bogomol'nyi bounds

Nuclear Physics B, 2016
An important question concerning the classical solutions of the equations of motion arising in quantum field theories at the BPS critical coupling is whether all finite-energy solutions are necessarily BPS.
Shouxin Chen, Yisong Yang
doaj   +2 more sources

The k-Hessian Equation

, 2009
Abstract The k-Hessian is the k-trace, or the kth elementary symmetric polynomial of eigenvalues of the Hessian matrix. When k ≥ 2, the k-Hessian equation is a fully nonlinear partial differential equations. It is elliptic when restricted to k-admissible functions. In this paper we establish the existence and regularity of k-admissible solutions to the
Gursky, Matthew, Lanconelli, Ermanno, Malchiodi, Andrea, Tarantello, Gabriella, Wang, Xu-Jia, Yang, Paul   +5 more
core   +4 more sources

Parabolic Hessian Quotient Equation in Exterior Domain

Mathematics
This study mainly focuses on the parabolic Hessian quotient equation in the exterior domain. The existence and uniqueness of generalized parabolically symmetric solutions with generalized asymptotic behavior are proven using Perron’s method.
Huawei Zhao, Limei Dai
doaj   +2 more sources

k-Hessian curvature type equations in space forms

Electronic Journal of Differential Equations, 2022
In this article, we study closed star-shaped (eta, k)-convex hypersurfaces in space forms satisfying a class of k-Hessian curvature type equations. Firstly, using the maximum principle, we obtain a priori estimates for the class of Hessian curvature type
Jundong Zhou
doaj   +1 more source

Radial solutions for fully nonlinear elliptic equations of Monge–Ampère type

Boundary Value Problems, 2021
First, the symmetry of classical solutions to the Monge–Ampère-type equations is obtained by the moving plane method. Then, the existence and nonexistence of radial solutions in a ball are got from the symmetry results.
Limei Dai, Huihui Cheng, Hongfei Li
doaj   +1 more source

Gradient estimate of the solutions to Hessian equations with oblique boundary value

Advanced Nonlinear Studies, 2022
In this paper, we study Hessian equations with the prescribed contact angle boundary value or oblique derivative boundary value and finally derive the a priori global gradient estimate for the admissible solutions.
Wang PeiHe
doaj   +1 more source