Boundary layers, Rellich estimates and extrapolation of solvability for elliptic systems (Q2921108)

In this paper, the authors consider boundary value problems of elliptic systems in divergence form on the upper half-space \(\mathbb R_+^{1+n}\), \(1+n\geq 2\). Assuming De Giorgi-type conditions and by introducing a new method which allows to treat each boundary value problem independently of the other ones, they study the extrapolation of solvability for related Neumann and Dirichlet problems. Indeed, the authors reprove the Regularity-Dirichlet duality principle between dual systems for solvability obtained in a previous work and extend it to \(H^1-\mathrm{BMO}\). Also they formulate and use a new duality principle for Neumann problems.