0
How to show that $f(x,y)=x^4+y^4-3xy$ is coercive ?
This is my attempt :
$$f(x,y)=x^4+y^4-3xy$$
$$f(x,y)=x^4+y^4\left(1-\frac{3xy}{x^4+y^4}\right)$$
As $||(x,y)|| \to \infty $ , $\frac{3xy}{x^4+y^4} \to 0$
So $||(x,y)|| \to \infty $ , $f(x,y)=x^4+y^4-3xy \to \infty$.
Is this a valid method ?...
In mathematics, a coercive function is a function that "grows rapidly" at the extremes of the space on which it is defined. Depending on the context different exact definitions of this idea are in use.
== Coercive vector fields ==
A vector field f : Rn → Rn is called coercive if
f
(
x
)
⋅
x
∥
x
∥
→
+
∞
as
...
4
1
After much delay, I have today removed the topology⇒general-topology tag synonym. This means that as of now topology is a perfectly acceptable stand-alone tag. Topology, of course, is also a wide ranging field of study, and I feel that the topology tag by itself often won't adequately narrow down...
0
