Regularity of the free boundary in a neighborhood of a contact point in the obstacle problem

The obstacle problem for an arbitrary linear elliptic equation is considered. The regularity of the boundary of the noncoincident set is studied in a neighborhood of a contact points of the boundary of a domain. The C1-regularity of the boundary and the continuity up to contact points of the second-order derivatives of the solution are proved. Bibliography: 3 titles. Translated fromProblemy Matematicheskogo Analiza, No. 19, 1999, pp. 101–104.