Improved Poincare inequalities with weights
Irene Drelichman, Ricardo G. Dur\'an

TL;DR
This paper establishes a generalized weighted Poincare inequality for bounded John domains, incorporating weights and boundary distance, extending previous inequalities with a unified approach.
Contribution
The paper introduces a new unified method to derive weighted Poincare inequalities on John domains, generalizing and extending known results.
Findings
Proves a weighted Poincare inequality involving weights and boundary distance.
Extends previous inequalities to more general weights and domain conditions.
Provides a unified approach applicable to various weighted inequalities.
Abstract
In this paper we prove that if is a bounded John domain, the following weighted Poincare-type inequality holds: where is a locally Lipschitz function on , denotes the distance of to the boundary of , the weights satisfy certain cube conditions, and depends on and . This result generalizes previously known weighted inequalities, which can also be obtained with our approach.
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