Some Problems Associated With A-harmonic Equations

This paper deals with the weak monotonicity property and higher integrability for A-harmonic functions. A new function space is introduced. Under some appropriate conditions, a weak monotonicity property is derived by using the new function space and Hodge decomposition. We also consider the nonhomogeneous A-harmonic equation with a measurable matrix G(x)∈GL(n) and a Radon measureμwith bounded total variation. A higher integrability result is derived by using the estimates for G-coefficients and Hodge decomposition. The results in this paper can be regarded as generalizations of the classical results.