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arXiv · 2108.00656

Parabolic weighted Sobolev-Poincar\'e type inequalities

Lars Diening·Mikyoung Lee·Jihoon Ok
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Abstract

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.

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Lars Diening, Mikyoung Lee, Jihoon Ok. 2021-08-02. Parabolic weighted Sobolev-Poincar\'e type inequalities. https://arxiv.org/abs/2108.00656

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