An estimate related to the Gagliardo-Nirenberg inequality
Moshe Marcus · Birkhäuser Basel eBooks · 1997
Let Ω be a domain of unit volume in ℝ n satisfying the cone condition, If u ∈ L ∞ (Ω) and ∥u∥ L ∞ ≠ 0, denote 1.1 $$ O(u): = {\left\| u \right\|_{{{L_{\infty }}}}}/{\left\| u \right\|_{{{L_1}}}}. $$ If u ≥ 0, the quantity O(u) is a measure of the ‘amplitude’ of u, i.e. of its deviation from a constant.