Results 21 to 30 of about 4,703 (266)

Completeness of Classical Thermodynamics: The Ideal Gas, the Unconventional Systems, the Rubber Band, the Paramagnetic Solid and the Kelly Plasma

Entropy, 2020
A method is developed to complete an incomplete set of equations of state of a thermodynamic system. Once the complete set of equations is found, in order to verify the thermodynamic validity of a system, the Hessian and entropy methods are exposed.
Karen Arango-Reyes, Gonzalo Ares de Parga   +1 more
doaj   +1 more source

G˚arding Cones and Bellman Equations in the Theory of Hessian Operators and Equations

Современная математика: Фундаментальные направления, 2017
In this work, we continue investigation of algebraic properties of G˚arding cones in the space of symmetric matrices. Based on this theory, we propose a new approach to study of fully nonlinear differential operators and second-order partial differential ...
N M Ivochkina, N V Filimonenkova
doaj   +1 more source

On a class of obstacle problem for Hessian equations on Riemannian manifolds

Journal of Inequalities and Applications, 2023
In this paper, we establish the a priori C 2 $C^{2}$ estimates for solutions of a class of obstacle problem for Hessian equations on Riemannian manifolds. Some applications are also discussed. The main contribution of this paper is the boundary estimates
Jinxuan Liu, Yong Wang
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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   +1 more source

A variational theory of the Hessian equation

Communications on Pure and Applied Mathematics, 2001
AbstractBy studying a negative gradient flow of certain Hessian functionals we establish the existence of critical points of the functionals and consequently the existence of ground states to a class of nonhomogenous Hessian equations. To achieve this we derive uniform, first‐ and second‐order a priori estimates for the elliptic and parabolic Hessian ...
Chou, Kai-Seng, Wang, Xu-Jia
openaire   +2 more sources

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
doaj   +1 more source

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.
openaire   +4 more sources

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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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
openaire   +2 more sources

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
openaire   +4 more sources