Gradient estimates for problems with Orlicz growth
Abstract We study a general nonlinear elliptic equation in the Orlicz setting with data not belonging to the dual of the energy space. We provide several Lorentz-type and Morrey-type estimates for the gradients of solutions under various conditions on the data.
In this paper we discuss the approximations introduced in the average-ion model usually employed for level population calculations. An improved system of equations of higher-order approximation is given. It is proved that in electric dipole approximation the level population probability Pnlj is independent of the quantum number j. leading to a great reduction of the number of equations to be solved. Finally, a method feasible for calculating these rate equations is suggested.