A variational inequality with mixed boundary conditions

In this paper we study a variational inequality for a second order uniformly elliptic operator on a bounded domain, the solution of which is required to lie above a given obstacle and to assume assigned values on a part of the boundary of the domain. We are mainly concerned with the regularity of the solution in relation to the regularity of the data. During the preparation of the paper the authors were partially supported by the Italian Consiglio Nazionale delle Ricerche, the first as visiting professor at the Scuola Normale Superiore (Pisa) on deputation from the Tata Institute of Fundamental Research (Bombay) and the second through the Istituto per l’Elaborazione dell’Informazione (Pisa).