Parabolic weighted Sobolev–Poincaré type inequalities. (May 2022) - Diening, Lars; Lee, Mikyoung; Ok, Jihoon
Abstract: We derive weighted Sobolev–Poincaré type inequalities in function spaces concerned with parabolic partial differential equations. We consider general weights depending on both space and time variables belonging to a Muckenhoupt class, so-called the parabolic A p -class, where only the parabolic cubes are involved in the definition.