Results 61 to 70 of about 8,395 (199)
MathematicsThe paper studies an unsteady equation with quadratic nonlinearity in second derivatives, that occurs in electron magnetohydrodynamics. In mathematics, such PDEs are referred to as parabolic Monge–Ampère equations.
Andrei D. Polyanin, Alexander V. Aksenov
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The Monge-Ampère equation: Hamiltonian and symplectic structures, recursions, and hierarchies [PDF]
, 2004 Using methods of geometry and cohomology developed recently, we study the Monge-Ampère equation, arising as the first nontrivial equation in the associativity equations, or WDVV equations. We describe Hamiltonian and symplectic structures as well as
Kersten, P.H.M. +2 more
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Dimer models and conformal structures
Communications on Pure and Applied Mathematics, Volume 79, Issue 2, Page 340-446, February 2026.Abstract Dimer models have been the focus of intense research efforts over the last years. Our paper grew out of an effort to develop new methods to study minimizers or the asymptotic height functions of general dimer models and the geometry of their frozen boundaries.
Kari Astala +3 more
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The complex Monge-Amp\`{e}re equation on some compact Hermitian manifolds
, 2014 We consider the complex Monge-Amp\`{e}re equation on compact manifolds when the background metric is a Hermitian metric (in complex dimension two) or a kind of Hermitian metric (in higher dimensions).
Chu, Jianchun
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Monge-Ampère Equation with Bounded Periodic Data [PDF]
Analysis in Theory and Applications, 2019 We consider the Monge-Ampere equation $\det(D^2u)=f$ in $\mathbb{R}^n$, where $f$ is a positive bounded periodic function. We prove that $u$ must be the sum of a quadratic polynomial and a periodic function. For $f\equiv 1$, this is the classic result by
Yanyan Li, Siyuan Lu
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The complex Monge-Ampère equation on compact Hermitian manifolds [PDF]
, 2009 We show that, up to scaling, the complex Monge-Ampere equation on compact Hermitian manifolds always admits a smooth solution.
Valentino Tosatti, B. Weinkove
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Inequalities and counterexamples for functional intrinsic volumes and beyond
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract We show that analytic analogs of Brunn–Minkowski‐type inequalities fail for functional intrinsic volumes on convex functions. This is demonstrated both through counterexamples and by connecting the problem to results of Colesanti, Hug, and Saorín Gómez.
Fabian Mussnig, Jacopo Ulivelli
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Life-Span of Classical Solutions to Hyperbolic Inverse Mean Curvature Flow
Discrete Dynamics in Nature and Society, 2020 In this paper, we investigate the life-span of classical solutions to hyperbolic inverse mean curvature flow. Under the condition that the curve can be expressed in the form of a graph, we derive a hyperbolic Monge–Ampère equation which can be reduced to
Zenggui Wang
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Removable Singularities of $m$-Hessian Equations
, 2016 In this paper we give a new, less restrictive condition for removability of singular sets, $E$, of smooth solutions to the m-Hessian equation (and also for more general fully nonlinear elliptic equations) in $\Omega \setminus E$, $\Omega \subset \mathbb ...
Car, Hülya, Pröpper, René
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On Multiscale RBF Collocation Methods for Solving the Monge–Ampère Equation
, 2020 This paper considers some multiscale radial basis function collocation methods for solving the two-dimensional Monge–Ampere equation with Dirichlet boundary. We discuss and study the performance of the three kinds of multiscale methods.
Zhiyong Liu, Qiuyan Xu
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