Unimprovable integral estimate for solutions of the Dirichlet problem for quasilinear elliptic equations of the second order in a neighborhood of an edge (Q2759331)

The article deals with solutions to the Dirichlet problem which contains the quasilinear elliptic nondivergent equation \(a_{ij}(x,u,u_x)u_{x_i x_j}+a(x, u, u_x)= 0,x\in G,\) and the boundary condition \(u(x)=0,x\in\partial G,\) where \( G \) is a domain from \({\mathbb R}^n. \) The boundary \( \partial G \supset \Gamma = {\bar \Gamma_1} \cup{\bar \Gamma_2}\) and \(\Gamma_1,\Gamma_2\) are enough smooth \((n-1)\)--dimensional surfaces such that \(\Gamma_1\cap\Gamma_2=\emptyset,\) \({\bar\Gamma_1}\cap{\bar\Gamma_2}=l.\) A theorem about integral estimation of the generalized solution to the Dirichlet problem in a neighborhood of the edge \(l\) is proved. The estimation is considered in a weight Sobolev space.