Results 171 to 180 of about 5,752 (197)

Serrin-Type Overdetermined Problems for Hessian Quotient Equations and Hessian Quotient Curvature Equations

The Journal of Geometric Analysis, 2023
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Zhenghuan Gao, Xiaohan Jia, Dekai Zhang
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Boundary Regularity for k-Hessian Equations

Acta Mathematica Sinica, English Series, 2023
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Li, You, Li, Meng Ni, Liu, Yan Nan
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Geometry of m-Hessian Equations

Journal of Mathematical Sciences, 2022
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Interior Hessian estimates for a class of Hessian type equations

Calculus of Variations and Partial Differential Equations, 2022
In this paper, the authors study the Hessian quotient equation \[ \frac{\sigma_k(\eta)}{\sigma_l(\eta)}=f(x) \] for combinatory indices \(k, l\), where \(\eta_i\equiv\Sigma_{j\not=i}\lambda_j\) and \(\lambda=(\lambda_1,\dots,\lambda_n)\) are the eigenvalues of the Hessian matrix \(D^2u\).
Chen, Chuanqiang, Dong, Weisong, Han, Fei   +2 more
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The Dirichlet problem for Hessian quotient equations in exterior domains

Journal of Mathematical Analysis and Applications, 2011
In this paper, we obtain the uniqueness and existence of viscosity solutions with prescribed asymptotic behavior at infinity to Hessian quotient equations in exterior ...
Limei Dai
exaly   +2 more sources

Stability of Serrin-Type Problem for Hessian Equations and Hessian Quotient Equations

Bulletin of the Malaysian Mathematical Sciences Society
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Sun, Yifan, Ma, Feiyao, Wo, Weifeng
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Hessian Estimate for Heat Equation

The Journal of Geometric Analysis, 2017
The author derives an interior Hessian estimate for the scalar heat equation on a complete Riemannian manifold \((M^n,g)\) which is independent of the covariant derivatives of the curvature. More precisely, assume that the curvature operator is bounded, \(|\mathrm{Rm}|\leq K\) on the geodesic ball \(B_p(\rho)\) centered at \(p\) and with radius \(\rho,\
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On symmetrization and Hessian equations

Journal d’Analyse Mathématique, 1989
A k-Hessian operator and k-Hessian integral \((k=1,...,n)\) are defined respectively by \[ S_ k(\nabla^ 2u)=\sum_{1\leq i_ ...
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Hessian equations in non-smooth domains

Nonlinear Analysis: Theory, Methods & Applications, 1999
This paper is concerned with the Dirichlet problem for \(k\)-Hessian equations \[ S_k(D^2u)=f\geq 0 \quad\text{in}\quad\Omega, \qquad u=h \quad\text{on}\quad\partial\Omega, \tag{\(*\)} \] where \(\Omega\) is a bounded domain in \({\mathbb R}^n\) and \(S_k(D^2u)\) denotes the \(k\)-th elementary symmetric function of the eigenvalues of \(D^2u\), \[ S_k ...
COLESANTI, ANDREA, SALANI, PAOLO
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Multiple solutions to Hessian equations

Manuscripta Mathematica, 2010
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