A remark on a generalization of a logarithmic Sobolev inequality to the Holder class

2009/08/22 by Hassan Ibrahim, Ibrahim, Hassan
Mathematics · #39B05 #42B25 #42B35 #54C35 #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.0908.3245

openalex publication_date 2009/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a recent work of the author, a parabolic extension of the elliptic Ogawa type inequality has been established. This inequality is originated from the Brezis-Gallouet-Wainger logarithmic type inequalities revealing Sobolev embeddings in the critical case. In this paper, we improve the parabolic version of Ogawa inequality by allowing it to cover not only the class of functions from Sobolev spaces, but the wider class of Holder continuous functions.

Citations

• The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations

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