Two-weight Caccioppoli inequalities for solutions of nonhomogeneous 𝐴-harmonic equations on Riemannian manifolds

Abstract

In this paper, we first prove the local two-weight Caccioppoli inequalities for solutions to the nonhomogeneous A A -harmonic equation of the form d ⋆ A ( x , d ω ) = B ( x , d ω ) d^{\star } A(x, d \omega ) =B(x,d\omega ) . Then, as applications of the local results, we prove the global two-weight Caccioppoli-type inequalities for these solutions on Riemannian manifolds.