On the analyticity of solutions to non-linear elliptic partial differential equations

Abstract

We give an easy proof of the fact that $C^{\infty }$ solutions to non-linear elliptic equations of second order $$\ddot{I}•(x,u,Du,D^{2}u)=0$$ are analytic. Following ideas of Kato, the proof uses an inductive estimate for suitable weighted derivatives. We then conclude the proof using Cauchy's method of majorants}.