Schauder estimates and existence theory for entire solutions of linear elliptic equations

Source abstract

Synopsis Existence as well as uniqueness theorems under certain growth conditions are given for entire solutions to linear elliptic equations in the n -dimensional space (2≦ n ). Introducing a proper norm, the proofs are based on a priori estimates. These estimates could be used to solve nonlinear equationsin the space, but the conditions on the nonlinearity have to be strong as the a priori estimates applyonly to classical, not to weak, solutions.