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1
vote
Implicit derivative?
In general you cannot even define $y(z)$ given generic functions $R$ and $L$.
If instead there exists $f$ such that $y=f(z)$ is satisfied for any point $\mathbf{x}=(x_1,...,x_n)$ then you have
$$
L(\ …
6
votes
1
answer
499
views
Estimating the flow when we know the vector field
Suppose we have a $C^k$ vector field $v$ and let $\phi_t$ be the corresponding flow. I have estimates on $v$ and its derivatives: $|v| < C_0$, $|Dv| < C_1$, $|D^2v| < C_2$, ... $|D^kv| < C_k$. My ques …