On regularity up to the boundary of solutions to degenerate nonlinear elliptic high-order equations

An operator A:Wm,pl,q (ν,μ,Ω)→(Wm,pl,q(ν,μ,Ω)) of the form Au = ∑ (-1)|α|DαAα (x,δmu), for |α|≤m, where Ω is a bounded open set of Rn, m≥3, p≥2, n>q>mp, ν and μ are positive functions in Ω, Wm,pl,q eν,μ,Ω) is the Banach space of all functions u:Ω→R with the properties |u|q, ν|Dαu|q, μ|Dβu|p∈L1(Ω), |α| = 1, |β| = m, and zero boundary values is considered. Hypothesis concerning exponents pα, functions ν,μ,να and the set Ω is proposed. Results in the investigation where proven to be correct.