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


Author: Shusen Ding
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 2367-2375
MSC (2000): Primary 35J60; Secondary 31C45, 58A10, 58J05
DOI: https://doi.org/10.1090/S0002-9939-04-07347-2
Published electronically: February 13, 2004
MathSciNet review: 2052415
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Shusen Ding
Affiliation: Department of Mathematics, Seattle University, Seattle, Washington 98122
Email: sding@seattleu.edu

DOI: https://doi.org/10.1090/S0002-9939-04-07347-2
Keywords: Caccioppoli inequalities, $A$-harmonic equations, manifolds, the two-weight
Received by editor(s): December 20, 2002
Received by editor(s) in revised form: May 6, 2003
Published electronically: February 13, 2004
Communicated by: Andreas Seeger
Article copyright: © Copyright 2004 American Mathematical Society

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