We prove a localization property of boundary sections for solutions to the Monge-Ampere equation. As a consequence we obtain pointwise C2,α estimates at boundary points under appropriate local conditions on the right hand side and boundary data.

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...

The graphics processing unit is a popular computing device for achieving exascale performance in high-performance programs, which used not only tasks, but also computational tasks such as machine learning, scientific computing, and cryptography. With the help of processor, you can achieve significant speed compared to central unit. CUDA, Compute Unified Device Architecture, software development...

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...