Results 81 to 90 of about 5,226,204 (223)
Non-Archimedean Green’s functions and Zariski decompositions
Comptes Rendus. MathématiqueWe study the non-Archimedean Monge–Ampère equation on a smooth projective variety over a discretely or trivially valued field. First, we give an example of a Green’s function, associated to a divisorial valuation, which is not $\mathbb{Q}$-PL (i.e. not a
Boucksom, Sébastien, Jonsson, Mattias
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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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On the integrability of a third-order Monge-Ampère type equation
, 1996 A third-order equation, similar to a Monge-Ampère equation, is studied, this being achieved by first converting the equation to a 3 × 3-hydrodynamics system.
Strachan, I.A.B., I.A.B. Strachan
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Aleksandrov-type estimates for a parabolic Monge-Ampere equation
Electronic Journal of Differential Equations, 2005 A classical result of Aleksandrov allows us to estimate the size of a convex function $u$ at a point $x$ in a bounded domain $Omega$ in terms of the distance from $x$ to the boundary of $Omega$ if $$int_{Omega} det D^{2}u , dx less than infty ...
David Hartenstine
doaj
Regularity of optimal mapping between hypercubes
Advanced Nonlinear Studies, 2023 In this note, we establish the global C3,α{C}^{3,\alpha } regularity for potential functions in optimal transportation between hypercubes in Rn{{\mathbb{R}}}^{n} for n≥3n\ge 3. When n=2n=2, the result was proved by Jhaveri.
Chen Shibing, Liu Jiakun, Wang Xu-Jia
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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, Qiu-Yan Xu
semanticscholar +1 more source
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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Well‐Posedness for Time‐Fractional Diffusion With Singular Multiplicative Forcing
Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.We consider a time‐fractional diffusion equation on ℝ with a possibly singular multiplicative forcing term. By exploiting an operator convolution identity, the original mild formulation is reduced to a Volterra integral equation involving the fractional diffusion family.
Ngo Ngoc Hung, Julian Pucheta
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Numerical solution of the Optimal Transportation problem using the Monge–Ampère equation
, 2014 International audienceA numerical method for the solution of the elliptic Monge–Ampère Partial Differential Equation, with boundary conditions corresponding to the Optimal Transportation (OT) problem, is presented.
Froese, Brittany D. +2 more
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Gevrey regularity of subelliptic Monge-Ampère equations in the plane
, 2011 In this paper, we establish the Gevrey regularity of solutions for a class of degenerate Monge–Ampère equations in the plane. Under the assumptions that one principal entry of the Hessian is strictly positive and the coefficient of the equation is ...
Xu, Chao-Jiang +3 more
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