Best Possible Estimates of Solutions to the Interface Problem for Linear Elliptic Divergence Second Order Equations in a Conical Domain

Let \(G\subset \mathbb {R}^n\) , \(n\geq 2\) be a bounded domain with the boundary \(\partial G\) that is a smooth surface everywhere except at the origin \(\mathcal {O}\in \partial G\) and near the point \(\mathcal {O}\) it is a conical surface with the vertex at \(\mathcal {O}\) . We assume that \(G=G_+\cup G_-\cup \Sigma _0\) is divided into two subdomains \(G_+\) and \(G_-\) by a \(\Sigma _0=G\cap \{x_n=0\},\) where \(\mathcal {O}\in \overline {\Sigma _0}\) .