What is the best constant in this special case of the Gagliardo--Nirenberg inequality?

Consider the special case of the Gagliardo--Nirenberg inequality in R^4 $$ \|u\|_p \le C_p \|\Delta u\|_2^{1-4/p} \|u\|_4^{4/p} $$ with $p \ge 4$. What is the value of the best constant $C_p$?

14 October 2021 1,145 5 View