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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.
Sep 8, 2015 · A continuous function $f(x)$ that is defined on $R^n$ is called coercive if $\lim\limits_{\Vert x \Vert \rightarrow \infty} f(x)=+ \infty$. I am finding it difficult to understand how the norm of these functions are computed in order to show that they are coercive.
Jan 17, 2023 · A function f: Rn → Rn is called coercive if f(x) ⋅ x ‖ x‖ → ∞ as ‖ x‖ → ∞. I came across this requirement in calculus of variations, where a coercivity condition is needed to show that a sequence of functions gamma-converges to some limiting function.
Definition. continuous function f : n. → R is coercive if. lim f(x) = ∞. ∥x∥→∞. Meaning : f(x) goes big if x grows. As x grows larger, it can “walk pass” any values, that’s why f has to be continuous in the definition. f can output ∞, the image of f is not R but the extended real R = R ∪ {±∞}.
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1. f(x; y) = x2 + y2. coercive. 2. f(x; y) = x4 + y4. 3xy = (x4 + y4)(1. x4 + y4: dominant. Hence coercive. 3. f(x; y; z) = ex2 + ey2 + ez2. 3xy. ) x4 + y4. x100 y100 z100. coercive since ex grows faster than xn. 4. f(x; y) = ax + by + c(ab 6= 0) not coercive. Proof: Let (x; y) satisfy ax + by = 0. Then. lim f(x; y) = c2. k(x;y)k!1.
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3 days ago · A bilinear functional phi on a normed space E is called coercive (or sometimes elliptic) if there exists a positive constant K such that phi(x,x)>=K||x||^2 for all x in E.
Sep 25, 2020 · A function $f$ defined on $\mathbb{R}^n$ is said to be coercive if $$\lim_{\|\vec{x}\|\rightarrow \infty}f(\vec{x})=+\infty.$$ I do not understand the idea of taking the limit as the norm approaches infinity.
