Strong solvability of a unilateral boundary value problem for nonlinear parabolic operators

Strong solvability in Sobolev spaces is proved for a unilateral boundary value problem for nonlinear parabolic operators. The operator is assumed to be of Caratheodory type and to satisfy a suitable ellipticity condition; only measurability with respect to the independent variable X is required. The main tools of the proof are an estimate for the second derivatives of functions which satisfy the unilateral boundary conditions and the mono-tonicity of the operator -u(t) with respect to Delta u for the same functions.