Parabolic weighted Sobolev-Poincaré type inequalities

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.

12pages, to appear in Nonlinear Analysis

References in corpus (2)

• Riesz potentials and nonlinear parabolic equations
• Gradient weighted norm inequalities for very weak solutions of linear parabolic equations with BMO coefficients