Schauder estimates and existence theory for entire solutions of linear elliptic equations
Heinrich Begehr, G. N. Hile · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1988
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.