# sobolev spaces – What is the optimal constant in an inequality?

My questions are that

1. What is & # 39;optimal& # 39; constant in an inequality? and
2. What is the difference between & # 39;sharp& # 39; and & # 39;optimal& # 39; constant?

In a paper theorem, it is given that

Let $$Omega subset mathbb R ^ n$$ to be a convex domain of diameter $$d$$ and $$u in W ^ {1,1} ( Omega)$$ such as $$int limits _ { Omega} u = 0.$$ then $${{} {1} {2} {Green} {Green} { {1} {1} {1} {1}$$
In addition, the constant $$frac {1} {2}$$ is optimal.

Any help is appreciated. Thank you.