Results 31 to 40 of about 5,752 (197)
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.
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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
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A Gradient Type Term for the k-Hessian Equation
The Journal of Geometric Analysis, 2023 In this paper, we propose a gradient type term for the $k$-Hessian equation that extends for $k>1$ the classical quadratic gradient term associated with the Laplace equation. We prove that such as gradient term is invariant by the Kazdan-Kramer change of variables.
Mykael Cardoso +2 more
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Boundary Value Problems, 2022 In this paper, we consider the exterior Dirichlet problem of Hessian equations σ k ( λ ( D 2 u ) ) = g ( x ) $\sigma _{k}(\lambda (D^{2}u))=g(x)$ with g being a perturbation of a general positive function at infinity. By estimating the eigenvalues of the
Limei Dai, Hongfei Li
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Asymptotic behavior of solutions of fully nonlinear equations over exterior domains
Comptes Rendus. Mathématique, 2021 In this paper, we consider the asymptotic behavior at infinity of solutions of a class of fully nonlinear elliptic equations $F(D^2u)=f(x)$ over exterior domains, where the Hessian matrix $(D^2u)$ tends to some symmetric positive definite matrix at ...
Jia, Xiaobiao
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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
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Maximum principles for viscosity solutions of weakly elliptic equations
Bruno Pini Mathematical Analysis Seminar, 2019 Maximum principles play an important role in the theory of elliptic equations. In the last decades there have been many contributions related to the development of fully nonlinear equations and viscosity solutions.
Antonio Vitolo
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Isogenies on twisted Hessian curves
Journal of Mathematical Cryptology, 2021 Elliptic curves are typically defined by Weierstrass equations. Given a kernel, the well-known Vélu's formula shows how to explicitly write down an isogeny between Weierstrass curves. However, it is not clear how to do the same on other forms of elliptic
Perez Broon Fouazou Lontouo +3 more
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International Journal of Mathematics and Mathematical Sciences, 2001 Solving systems of nonlinear equations and inequalities is of critical importance in many engineering problems. In general, the existence of inequalities in the problem adds to its difficulty.
Mahmoud M. El-Alem +2 more
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Three-dimensional large-scale aerodynamic shape optimization based on shape calculus
, 2013 Large-scale three-dimensional aerodynamic shape optimization based on the compressible Euler equations is considered. Shape calculus is used to derive an exact surface formulation of the gradients, enabling the computation of shape gradient information ...
Schmidt, Stephan +4 more
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