Two Weak Wt-classes Of Differential Forms And Weakly A-harmonic Tensors

A-harmonic equation is an important quasilinear ellipitc equation, which has signif-icant applications in quasiconformal analysis and nonlinear elasticity. There are closed connections between differential forms and its weak and very weak solutions, i.e., A-harmonic and weakly A-harmonic tensors. In this paper, we first introduce two weak WT-classes of differential forms and show the connections between these differential expressions and weakly A-harmonic tensors with different properties. Meanwhile, we obtain a weak reverse Holders inequality on weak WT2 class of differential forms by Hodge decomposition. Further, we give an alternative proof for the higher integrability result of weakly A-harmonic tensors due to B.Stroffolini.