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.

One of the most efficient methods for the study of boundary and periodic problems for nonlinear differential equations and inclusions, consists in the operator treatment of these problems in suitable functional spaces. However, for a number of problems of this sort, the maps constructed in functional spaces do not possess “nice” properties on the whole domain, but only on some open neighborhood...

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...