I have seen functional-completeness (in regards to boolean functions) defined as: A set X of truth-functions (of 2-valued logic) is functionally complete if and only if for each of the five defined classes, there is a member of X which does not belong to that class With those 5 classes being: ...

Could anyone see how the following two lines follow from Gronwall lemma? I use the usual differential form gronwall lemma from in Evans book. I do not know how to deal with the term involves the sobolev norm $|\cdot|_1$. I think that, if the second term on the lhs can ve removed, then the rhs s...

During my research I came across a weak gronwall-type inequality of the following type: $$-\int_0^T f'(t)(u(t)-u_0) \leq \int_0^T f(t)u(t)$$ for non-negative $f\in C_c^\infty(0,T)$, $u\in L^1(0,T)$ and $u_0$ a number. From such a "weak Gronwall inequality" one can conclude that $$ u(t^*) \leq u...

If I have that $$||\eta_u(t)||\leq 1+C_1\int_0^t \frac{1}{||\eta(s)||}||\eta_u(s)||ds$$ and $$\sqrt{1-\frac{2\varepsilon}{C}}||u||\leq ||\eta(s)||\leq 2||u||$$ how to obtain using the Gronwall inequality that $$\displaystyle ||\eta_u(t)||\leq 1+\exp\left(\frac{2C_1}{||u||}t\right)$$ Thank you.