Results 261 to 270 of about 1,227,664 (287)

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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Singular Quasilinear and Hessian Equations and Inequalities

Journal of Functional Analysis, 2009
We solve the existence problem in the renormalized, or viscosity sense, and obtain global pointwise estimates of solutions for quasilinear and Hessian equations with measure coefficients and data, including the following model problems:−Δpu=σuq+μ,Fk[−u ...
Phuc Cong Nguyen, Igor Verbitsky
exaly   +2 more sources

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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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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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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