Results 61 to 70 of about 5,226,204 (223)
Exponential convergence for ultrafast diffusion equations with log‐concave weights
Bulletin of the London Mathematical Society, Volume 58, Issue 9, September 2026.Abstract We study the asymptotic behavior of a weighted ultrafast diffusion PDE on the real line, with a log‐concave and log‐lipschitz weight, and prove exponential convergence to equilibrium. This result goes beyond the compact setting studied in Iacobelli [Discrete Contin. Dyn. Syst. 39 (2019), 4929–4943].
Max Fathi, Mikaela Iacobelli
wiley +1 more source
Singularity of non‐pluripolar cohomology classes
Bulletin of the London Mathematical Society, Volume 58, Issue 9, September 2026.Abstract We establish a relation between Lelong numbers and the full mass property of relative non‐pluripolar products. We use this relation to prove that if the restricted volume of a big class α$\alpha$ along an effective divisor D$D$ has full mass, then the Lelong numbers of the non‐pluripolar class ⟨αn−1⟩$\langle \alpha ^{n-1}\rangle$ at every ...
Duc‐Bao Nguyen +2 more
wiley +1 more source
A Parabolic Monge–Ampère Type Equation of Gauduchon Metrics
, 2017 We prove the long time existence and uniqueness of solution to a parabolic Monge–Ampère type equation on compact Hermitian manifolds. We also show that the normalization of the solution converges to a smooth function in the smooth topology as $t ...
Tao Zheng
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On the symplectic structure deformations related to the Monge–Ampère equation on the Kähler manifold P2(C) [PDF]
, 2023 We analyze the cohomology structure of the fundamental two-form deformation related to a modified Monge–Ampère type on the complex Kähler manifold P2(C).
Prykarpatski, A. K. +7 more
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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
doaj +1 more source
Approximate Ricci‐Flat Metrics for Calabi–Yau Manifolds
Fortschritte der Physik, Volume 74, Issue 7, July 2026.ABSTRACT We outline a method to determine analytic Kähler potentials with associated approximately Ricci‐flat Kähler metrics on Calabi–Yau manifolds. Key ingredients are numerically calculating Ricci‐flat Kähler potentials via machine learning techniques and fitting the numerical results to Donaldson's ansatz.
Seung‐Joo Lee, Andre Lukas
wiley +1 more source
, 2016 Now in its second edition, this monograph explores the Monge-Ampère equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory of weak solutions, including regularity ...
Gutiérrez, Cristian E
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Wall–chamber decompositions for generalised Monge–Ampère equations
Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.Abstract Generalised Monge–Ampère (gMA) equations form a large class of PDE including Donaldson's J‐equation, inverse Hessian equations, some supercritical deformed Hermitian–Yang–Mills (dHYM) equations and some Z‐critical equations. Solvability of these equations is characterised by numerical criteria involving intersection numbers over all ...
Sohaib Khalid +1 more
wiley +1 more source
The Monge–Ampère equation and its link to optimal transportation [PDF]
, 2013 We survey old and new regularity theory for the Monge-Ampere equation, show its connection to optimal transportation, and describe the regularity properties of a general class of Monge-Ampere type equations arising in that context.
G. De Philippis, A. Figalli
semanticscholar +1 more source
Global regularity for the Monge-Ampère equation with natural boundary condition [PDF]
Annals of Mathematics, 2018 In this paper, we establish the global $C^{2,\alpha}$ and $W^{2,p}$ regularity for the Monge-Amp\`ere equation subject to a natural boundary condition arising in optimal transportation.
Shi-Bing Chen, Jia-Kun Liu, Xu-Jia Wang
semanticscholar +1 more source