We introduce a non local analog to the Monge-Ampere operator and show some of its properties. We prove that a global problem involving this operator has C solutions in the full space.

Disturbance of the Maxwellian plasma may occur in the vicinity of a spacecraft due to photoemission, interactions between the spacecraft and thermospheric gases, or electron emissions from other devices on the spacecraft. Significant non-Maxwellian plasma distributions may also occur in nature as a mixture of ionospheric and magnetospheric plasmas or secondaries produced by photoionization in t...

X (F ωM ) , 2 we have the following: (1) (Apriori estimate) Suppose u is a weak solution in PSHF∗ωM (X) ∩ L(X) of the equation with the normalization supX u = 0, then there is a constant C such that ‖u‖L∞ ≤ C‖f‖Lp where C only depend on F , ω and p; (2) There would always be a bounded solution for this equation; (3) If F is locally birational, then any bounded solution is actually the unique co...

We prove that global Lipschitz solutions to the linearized MongeAmpere equation Lφu := ∑ φuij = 0 must be linear in 2D. The function φ is assumed to have the Monge-Ampere measure detD2φ bounded away from 0 and ∞.

A model for incomplete reconnection in sawtooth crashes is presented. The reconnection inflow during the crash phase of sawteeth self-consistently convects the high pressure core toward the reconnection site, raising the pressure gradient there. Reconnection shuts off if the diamagnetic drift speed at the reconnection site exceeds a threshold, which may explain incomplete reconnection. The rela...

We use a localization property of boundary sections for solutions to the Monge-Ampere equation and obtain global W 2,p estimates under natural assumptions on the domain and boundary data.

We consider a class of Monge–Ampere equations where the convex conjugate of the unknown function is prescribed on a boundary of its domain yet to be determined. We show the existence of a weak solution.