Special Session 73: Nonlinear elliptic and parabolic equations and related functional inequalities
Deficit estimates for an entropic form of Gagliardo-Nirenberg inequalities related to nonlinear diffusion equations and their application
Takeshi Suguro
Kumamoto University Japan
Co-Author(s):
Abstract:
We consider functional inequalities concerning the $p$-Laplace equation. In this talk, we introduce an entropic form of the Gagliardo--Nirenberg inequalities based on the Tsallis entropy, a one-parameter extension of the Boltzmann--Shannon entropy. We obtain deficit estimates for the inequality and consider their application to the uncertainty relation inequality.