Gm. Lieberman, Regularity of solutions of obstacle problems for elliptic equations with oblique boundary conditions, PAC J MATH, 201(2), 2001, pp. 389-419
Much has been written about various obstacle problems in the context of var
iational inequalities. In particular, if the obstacle is smooth enough and
if the coefficients of associated elliptic operator satisfy appropriate con
ditions, then the solution of the obstacle problem has continuous rst deriv
atives. For a general class of obstacle problems, we show here that this re
gularity is attained under minimal smoothness hypotheses on the data and wi
th a one-sided analog of the usual modulus of continuity assumption for the
gradient of the obstacle. Our results apply to linear elliptic operators w
ith Holder continuous coefficients and, more generally, to a large class of
fully nonlinear operators and boundary conditions.