On the Existence of Strong Solutions for a Degenerate Parabolic Inequality with Mixed Boundary Conditions

Abstract

The degenerate parabolic variational inequality with mixed boundary conditions and inhomogeneous initial conditions is studied in the case where the corresponding operator can lose the properties of coercivity and continuity in the corresponding Sobolev spaces. By using the Hardy–Poincaré inequality, we prove the unique solvability of the original evolutionary variational inequality under the condition that the degenerate weight function is a function of potential type.