[再寄小读者之数学篇](2014-05-28 Ladyzhenskaya 不等式)

$$\bex f\in C_c^\infty(\bbR^2)\ra \sen{f}_{L^4}\leq \sqrt{2} \sen{f}_{L^2}^{1/2} \sen{\p_1f}_{L^2}^{1/4} \sen{\p_2f}_{L^2}^{1/4}, \eex$$ $$\bex f\in C_c^\infty(\bbR^3)\ra \sen{f}_{L^4}\leq 2^{3/4} \sen{f}_{L^2}^{1/4} \sen{\p_1f}_{L^2}^{1/4} \sen{\p_2f}_{L^2}^{1/4} \sen{\p_3f}_{L^2}^{1/4}. \eex$$