Existence and regularity results for oblique derivative problems for heat equation in an angle

An initial-boundary-value problem is considered for the heat equation in an infinite angle d(theta T) subset of or equal to R-2 x [0, infinity) with the oblique derivative boundary conditions on the faces y(i) of the angle: partial derivative u/partial derivative n + h(i) partial derivative u/partial derivative r = phi(i) on gamma(i), i = 0, 1, with either h(0) + h(1) > 0, or h(0) + h(1) less than or equal to 0. The unique solvability of such a problem is proved in appropriate weighted Sobolev spaces according to the sign of h(0) + h(1). Estimates of the solution are obtained under 'natural' restrictions on the opening of the angle.