Parabolic weighted Sobolev–Poincaré type inequalities

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 Ap-class, where only the parabolic cubes...

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Bibliographic Details
Published in:Nonlinear analysis 2022-05, Vol.218, p.112772, Article 112772
Main Authors: Diening, Lars, Lee, Mikyoung, Ok, Jihoon
Format: Article
Language:English
Subjects:
Parabolic equation
Parabolic Muckenhoupt class
Sobolev–Poincaré inequality
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Summary: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 Ap-class, where only the parabolic cubes are involved in the definition.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2021.112772