# Several Basic Inequalities for PDEs

In mathematics, especially in analysis and PDEs, we evaluate or compare some mathematical quantities in order to reach a desired conclusion. Of course, equality is the best one, however, in many situations we cannot reach our goal only with equalities. … Continue reading

# A Simple Proof of Gronwall’s Inequality

[latexpage] This post introduces a simple proof of Gronwall’s inequality (Thomas Hakon Gronwall, 1877~1932) of the integral form. Let $\alpha, \beta, u \in C^0([a,b])$ with $a<b$. Assume that $\beta \geqslant 0$ on $[a,b]$. Suppose that  u(t) \leqslant \alpha … Continue reading