The behavior near the boundary corner point of solutions to the degenerate oblique derivative problem for elliptic second-order equations in a plane domain (Q1932451)

The oblique derivative problem for general second-order linear elliptic operators is studied, with degeneracy given by the boundary condition. A priori estimates of the solution are given in the Kondratiev spaces. The power modulus of the continuity of solutions at the angular point of the boundary of a plane bounded domain is estimated. The novelty is a solution estimate for the equations with almost minimal smooth coefficients. The main tool is given by some Friedrichs-Wirtinger type inequalities, involving the eigenvalues of a specific eigenvalue problem related with a particular corner-type domain. In the last part some examples are given, proving that the regularity assumptions on the coefficients are crucial for the obtained estimates.