Results 241 to 250 of about 4,703 (266)

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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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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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 and symmetrization

2005
In this paper we state same comparisons results for solutions to Hessian type equations in dimension n> 2. These results involve convenient rearrangements of solutions that preserve suitable cross-sectional measures of their level sets.
BRANDOLINI, BARBARA, TROMBETTI, CRISTINA
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Multiple solutions to Hessian equations

Manuscripta Mathematica, 2010
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Weak solutions of hessian equations

Communications in Partial Differential Equations, 1997
We consider the existence, uniqueness and Holder regularity of weak solutions of Hessian equations, determined by the elementary symmetric functions, with Lp inhomogeneous terms. The notion of weak solution is defined by approximation and our treatment draws on the classical theory, together with recent Lp estimates resulting from our isoperimetric ...
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Pogorelov type C2 estimates for Sum Hessian equations and a rigidity theorem

Journal of Functional Analysis, 2023
Changyu Ren
exaly  

On the Dirichlet problem for general augmented Hessian equations

Journal of Differential Equations, 2020
Feida Jiang, Neil S Trudinger
exaly  

Radial symmetry and monotonicity of the positive solutions for k-Hessian equations

Applied Mathematics Letters, 2023
Lihong Zhang
exaly