The information-theoretic meaning of Gagliardo–Nirenberg type inequalities
Giuseppe ToscaniUniversità di Pavia, Italy
Gagliardo–Nirenberg inequalities are interpolation inequalities which were proved independently by Gagliardo and Nirenberg in the late fifties. In recent years, their connections with theoretic aspects of information theory and nonlinear di¤usion equations allowed to obtain some of them in optimal form, by recovering both the sharp constants and the explicit form of the optimizers. In this note, at the light of these recent researches, we review the main connections between Shannon-type entropies, di¤usion equations and a class of these inequalities.
Cite this article
Giuseppe Toscani, The information-theoretic meaning of Gagliardo–Nirenberg type inequalities. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 30 (2019), no. 2, pp. 237–253DOI 10.4171/RLM/845