On the variational inequalities for certain convex function classes

Abstract

The existence and the C1,alpha regularity of the weak solution to the variation inequality -(a(i)(x, u, delu))xi - (g(i)(x,u))xi + b(x,u, delu) greater-than-or-equal-to 0 with respect to a closed convex function class is proved. For the regularity, we use the fact that the regularity for the viscosity solutions to the Hamilton-Jacobi equations implies the C1,alpha interior regularity of the solution to the bilateral obstacle problem which in turn gives that of the solution to the variational inequality. (C) 1995 Academic Press, Inc.