Abstract
In this paper, we prove both the local and global Lφ -norm inequalities for Green's operator applied to minimizers for functionals defined on differential forms in Lφ -averaging domains. Our results are extensions of Lp norm inequalities for Green's operator and can be used to estimate the norms of other operators applied to differential forms.
Highlights
Let Ω be a bounded domain in Rn, n ≥ 2, B and s B with s > 0 be the balls with the same center and diam(s B) = sdiam(B) throughout this paper
Lebesgue measure of a set E ⊆ Rn is expressed by |E|
We denote the average of u over
Summary
Let u ∈ Wl1o,c1( , 0)be a k-quasi-minimizer for the functional (2.1), be a Young function in the class G(p, q, C), 1 ≤ p
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