Parabolic weighted Sobolev-Poincar\'e type inequalities

Jihoon Ok; Lars Diening; Mikyoung Lee

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Parabolic weighted Sobolev-Poincar\'e type inequalities

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arxiv 2108.00656 v2 pith:LCPOGSXF submitted 2021-08-02 math.AP

Parabolic weighted Sobolev-Poincar\'e type inequalities

Lars Diening , Mikyoung Lee , Jihoon Ok This is my paper

classification math.AP

keywords parabolicclassinequalitiessobolev-poincartypeweightedbelongingconcerned

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We derive weighted Sobolev-Poincar\'e 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.

Parabolic weighted Sobolev-Poincar\'e type inequalities

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