Dirichlet problem for degenerate elliptic complex Monge-Ampere equation
Electronic Journal of Differential Equations, 2004 We consider the Dirichlet problem $$ det ig({frac{partial^2u}{partial z_ipartial overline{z_j}}} ig)=g(z,u)quadmbox{in }Omega,, quad uig|_{ partial Omega }=varphi,, $$ where $Omega$ is a bounded open set of $mathbb{C}^{n}$ with regular boundary, $g$ and $
Saoussen Kallel-Jallouli
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Symmetries, Reductions and Exact Solutions of Nonstationary Monge–Ampère Type Equations
MathematicsA family of strongly nonlinear nonstationary equations of mathematical physics with three independent variables is investigated, which contain an arbitrary degree of the first derivative with respect to time and a quadratic combination of second ...
Alexander V. Aksenov, Andrei D. Polyanin
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Boundary blow-up solutions to the Monge-Ampère equation: Sharp conditions and asymptotic behavior
Advances in Nonlinear Analysis, 2019 Consider the boundary blow-up Monge-Ampère ...
Zhang Xuemei, Feng Meiqiang
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Schouten tensor equations in conformal geometry with prescribed boundary metric
Electronic Journal of Differential Equations, 2005 We deform the metric conformally on a manifold with boundary. This induces a deformation of the Schouten tensor. We fix the metric at the boundary and realize a prescribed value for the product of the eigenvalues of the Schouten tensor in the interior ...
Oliver C. Schnuerer
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The Föppl-von Kármán equations of elastic plates with initial stress. [PDF]
R Soc Open Sci, 2022 Ciarletta P, Pozzi G, Riccobelli D.
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Removable singular sets of fully nonlinear elliptic equations
Electronic Journal of Differential Equations, 1999 In this paper we consider fully nonlinear elliptic equations, including the Monge-Ampere equation and the Weingarden equation. We assume that $F(D^2u, x) = f(x) quad x in Omega,,$ $u(x) = g(x) quad xin partial Omega $ has a solution $u$ in $C^2(Omega ...
Lihe Wang, Ning Zhu
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Contact Geometry of Hyperbolic Equations of Generic Type
Symmetry, Integrability and Geometry: Methods and Applications, 2008 We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampère (class 6-6), Goursat (class 6-7) and generic (class 7-7 ...
Dennis The
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Cortical Morphometry Analysis based on Worst Transportation Theory. [PDF]
Inf Process Med Imaging, 2021 Zhang M +7 more
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Global interval bifurcation and convex solutions for the Monge-Ampere equations
Electronic Journal of Differential Equations, 2018 In this article, we establish the global bifurcation result from the trivial solutions axis or from infinity for the Monge-Ampere equations with non-differentiable nonlinearity. By applying the above result, we shall determine the interval of $\gamma$
Wenguo Shen
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Design of freeform mirrors using the concentric rings method. [PDF]
Heliyon, 2023 González-García J +2 more
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