Weighted Decomposition Estimates for Differential Forms

Abstract

Ω -weighted Caccioppoli-type estimates for A-harmonic tensors. Furthermore, by Whitney covering lemma, we obtain the global results in domain Ω ⊂ R n . These results can be used to study the integrability of differential forms and to estimate the integrals for differential forms.

The existence of solutions to the nonhomogeneous "Equation missing" -harmonic equation

“…If f = 0, the equation (2.1) degenerates into the homogeneous A-harmonic equation [4][5][6][7][8][9][10].…”

Higher Integrability for Very Weak Solutions of InhomogeneousA-Harmonic Form Equations

“…Lots of results have been obtained in recent years about different versions of the -harmonic equation; see [1][2][3][4][5][6][7][8][9][10][11][12][13].…”

Zeros for the Gradients of WeaklyA-Harmonic Tensors

“…There has been remarkable work [1][2][3][4][5][6][7][8][9][10] in the study of (1). When is a 0-form, that is, is a function, (1) is equivalent to div ( , ∇ ) = 0.…”