It sounds like you're asking: Given a differential equation with boundary conditions and a solution to that, can I conclude that this is the only such solution?
So I know in 2D you have that holomorphic and harmonic functions are related, but is there any particularly interesting thing about it in higher dimensions? Like what information does it carry about a function/are there any nifty theorems about it?
@AkivaWeinberger finelly i don't understand what is the relation between $\frac{a-b}{2}\in K$ and $||\frac{a-b}{2}||^2\leq ||x-a||^2-||x-\frac{a+b}{2}||^2\leq0$
as orbit says, "x times" really only makes sense for integer x, and when you take the derivative x takes values on a continuum, including noninteger points
I looked at Sage (big 3 GB package, but no easy IDE out of the box!) and many others, but none of them would be easy to use for undergrad in economics (my students) who have zero knowledge about programming
I know how to use the Weierstass-M test to prove uniform convergence, is there a way to use something like it to show non-uniform convergence? In general how do I prove non-uniform convergence?
@GFauxPas it's somewhat situation dependent. You could try direct stuff, for example by showing that its maximum is bounded away from the function in question over all $n$. Sometimes you can do so by showing that it breaks certain rules such as the integrals converging nicely, or that the limit is not continuous
Let $E = \mathbb{Q} \cap [0,1]$. Let $f: E \rightarrow \mathbb{R}$. If $f$ has two continuous extensions $g,h$, show that $g(x) = h(x)$ for all $x \in [0,1]$.
Question, anybody: If I take the derivative of a solution of a PDE w.r.t. to a parameter, to be precise $\nabla_m u$ where $(\omega m + \partial^2/{\partial x^2})u = q$, where $u$ is the solution, and $m$ the parameter, can I just "take the derivative" of the PDE?
