Results 21 to 30 of about 1,563,827 (90)
Weak solutions of equations of complex Monge-Ampère type [PDF]
, 2000 We prove some existence results for equations of complex Monge-Ampère type in strictly pseudoconvex domains and on Kähler ...
Kołodziej, Sławomir +1 more
core +1 more source
Free boundary Monge-Ampère equations
, 2022 In this paper, we consider a class of Monge-Ampère equations in a free boundary domain of ℝ2 where the value of the unknown function is prescribed on the free boundary.
Marc Sedjro
core +1 more source
On the integrability of a class of Monge-Ampère equations [PDF]
, 2001 We give the Lax representations for the elliptic, hyperbolic and homogeneous second order Monge-Ampère equations. The connection between these equations and the equations of hydrodynamical type give us a scalar dispersionless Lax representation. A matrix
GÜRSES, METİN +6 more
core +1 more source
Mirrors, lenses and Monge–Ampère equations
, 2021 International audienceIs it possible to shape a piece of glass so that it refracts and concentrates sunlight in order to produce a given image? The modelling of this kind of problem leads to nonlinear second-order partial differential equations, which ...
Mérigot, Quentin, Thibert, Boris
core +1 more source
Attractors and Finite‐Dimensional Behaviour in the 2D Navier‐Stokes Equations
International Scholarly Research Notices, Volume 2013, Issue 1, 2013., 2013 The purpose of this review is to give a broad outline of the dynamical systems approach to the two‐dimensional Navier‐Stokes equations. This example has led to much of the theory of infinite‐dimensional dynamical systems, which is now well developed.
James C. Robinson +3 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 $t ...
Tao Zheng
core +1 more source
An adaptive method for the numerical solution of a 2D Monge-Ampère equation [PDF]
, 2021 Parabolic fully nonlinear equations may be found in various applications,for instance in optimal portfolio management strategy. We focus here on a canonical parabolic Monge-Ampère equationin two space dimensions.
Gourzoulidis, Dimitrios +5 more
core +1 more source
Viscosity solutions of fully nonlinear functional parabolic PDE
International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 22, Page 3539-3550, 2005., 2005 By the technique of coupled solutions, the notion of viscosity solutions is extended to fully nonlinear retarded parabolic equations. Such equations involve many models arising from optimal control theory, economy and finance, biology, and so forth. The comparison principle is shown.
Liu Wei-an, Lu Gang
wiley +1 more source
Cohomogeneity‐one solitons in Laplacian flow: Local, smoothly‐closing and steady solitons
Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.Abstract We initiate a systematic study of cohomogeneity‐one solitons in Bryant's Laplacian flow of closed G2$\text{G}_2$‐structures on a 7‐manifold, motivated by the problem of understanding finite‐time singularities of that flow. Here, we focus on solitons with symmetry groups Sp(2)${\rm Sp}(2)$ and SU(3)${\rm SU}(3)$; in both cases, we prove the ...
Mark Haskins, Johannes Nordström
wiley +1 more source
A Miyaoka–Yau inequality for hyperplane arrangements in CPn$\mathbb {CP}^n$
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract Let H$\mathcal {H}$ be a hyperplane arrangement in CPn$\mathbb {CP}^n$. We define a quadratic form Q$Q$ on RH$\mathbb {R}^{\mathcal {H}}$ that is entirely determined by the intersection poset of H$\mathcal {H}$. Using the Bogomolov–Gieseker inequality for parabolic bundles, we show that if a∈RH$\mathbf {a}\in \mathbb {R}^{\mathcal {H}}$ is ...
Martin de Borbon, Dmitri Panov
wiley +1 more source