Prefer a chat interface with context about you and your work?
Interpolation inequalities in <inline-formula><tex-math id="M1">\begin{document}$ \mathrm W^{1,p}( {\mathbb S}^1) $\end{document}</tex-math></inline-formula> and <i>carré du champ</i> methods
This paper is devoted to an extension of rigidity results for nonlinear differential equations, based on carré du champ methods, in the one-dimensional periodic case. The main result is an interpolation inequality with non-trivial explicit estimates of the constants in $ \mathrm W^{1,p}( {\mathbb S}^1) $ with $ p\ge2 $. …