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

Ding, Shusen

doi:10.1090/S0002-9939-04-07347-2

Two-weight Caccioppoli inequalities for solutions of nonhomogeneous $A$-harmonic equations on Riemannian manifolds
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Proc. Amer. Math. Soc. 132 (2004), 2367-2375 Request permission

Abstract:

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

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