Smoothness of solutions of a special one-sided problem

Abstract

We consider a planar domain, namely a curvilinear quadrilateral. We study a variational inequality of special form on the set of functions that are monotonically increasing on part of the boundary. This problem corresponds to a one-sided problem for an elliptic equation. A boundary condition of first kind is prescribed on part of the boundary, while on the other part of the boundary the tangential derivative is nonnegative and the product of the tangential and oblique derivatives is zero. We establish that the first derivatives of the solution satisfy a Hölder condition. Bibliography: 5 titles.