Some Caccioppoli Estimates for Differential Forms

Abstract

We prove the global Caccioppoli estimate for the solution to the nonhomogeneous A-harmonic equation d∗A(x,u,du)=B(x,u,du), which is the generalization of the quasilinear equation divA(x,u,∇u)=B(x,u,∇u). We will also give some examples to see that not all properties of functions may be deduced to differential forms.