Meyers–Serrin theorem

The Meyers–Serrin theorem is a result in the field of partial differential equations, specifically concerning weak solutions of parabolic equations. It provides conditions under which weak solutions exist and are defined in a specific sense. More precisely, the theorem establishes criteria for the existence of weak solutions to the initial boundary value problem for nonlinear parabolic equations. It relates to the properties of the spaces involved, particularly Sobolev spaces, and the concept of weak convergence.