November 11, 2025Monatshefte für MathematikOpen Access

Note on the Poincaré and Friedrichs Inequalities in Sobolev Spaces with Variable Exponents

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Poincaré inequality was explored in the context of Sobolev spaces with variable exponents, highlighting its significance.
The finite Lebesgue measure of the open set Ω plays a crucial role in establishing these inequalities.
Analysis utilized Sobolev spaces, offering insights into new inequality variants and further mathematical implications.
These findings may enhance understanding in functional analysis, promoting more flexible mathematical frameworks.

Implication

This article demonstrates Poincaré inequality variants in Sobolev spaces, suggesting implications for Friedrichs-type inequalities.

Abstract

The aim of this article is to study a variant of the Poincaré inequality in Sobolev spaces Wk,p(· )(Ω ) W k , p ( · ) ( Ω ) where Ω Ω is a given open set of Rⁿ R n with finite Lebesgue measure and, consequently, the Friedrichs type inequality.

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Cite This Study

Viszus et al. (2025) studied this question.

synapsesocial.com/papers/69252e9ec0ce034ddc3565a8 https://doi.org/10.1007/s00605-025-02133-7

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Implication

This article demonstrates Poincaré inequality variants in Sobolev spaces, suggesting implications for Friedrichs-type inequalities.

Note on the Poincaré and Friedrichs Inequalities in Sobolev Spaces with Variable Exponents

Key Points

Implication

Abstract

Discussion

Cite This Study

Note on the Poincaré and Friedrichs Inequalities in Sobolev Spaces with Variable Exponents

Key Points

Implication

Abstract

Discussion

Cite This Study

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