We investigate the sharp constants in a Brézis-Gallouët-Wainger type inequality with a double logarithmic term in the Hölder space in a bounded domain in Rn. Ibrahim, Majdoub and Masmoudi gave the sharp constant in the two-dimensional case. We make precise estimates to give the sharp constants, and pass to the case of higher dimensions n ≥ 2. We can also show that the inequality with fixed constants including the sharp ones admits an extremal function under a suitable condition when the domain is a ball. © 2010 Elsevier Ltd. All rights reserved.
CITATION STYLE
Morii, K., Sato, T., & Wadade, H. (2010). Brézis-Gallouët-Wainger type inequality with a double logarithmic term in the Hölder space: Its sharp constants and extremal functions. Nonlinear Analysis, Theory, Methods and Applications, 73(6), 1747–1766. https://doi.org/10.1016/j.na.2010.05.012
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