Gagliardo-Nirenberg interpolation inequality

The Gagliardo-Nirenberg interpolation inequality is a mathematical concept developed by Louis Nirenberg and Emilio Gagliardo. Nirenberg, a Canadian-born American mathematician, was recognized for his work in analysis, particularly with partial differential equations. He shared the Abel Prize in 2015 with John F. Nash, Jr..1

The Gagliardo-Nirenberg inequality relates different norms of a function, essentially providing bounds on certain derivatives of a function based on other derivatives and the function itself. This type of inequality is fundamental in the study of partial differential equations and functional analysis, helping to establish properties of solutions and understand their behavior.12