EDB β€” 1H1

↑ ← β†’ ↓ view in whole PDF view in whole HTML

View

English

Exercises

  1. [1H1] In the same hypotheses of the exercise [1GZ], we also assume that f∈C1(A).

    • We decompose y=(yβ€²,yn),βˆˆβ„n as we did for x. We define the function G:V→ℝn as G(y)=(yβ€²,g~(y)). Let W=G(V) be the image of V, show that WβŠ†U and that W is open.

    • Show that is G:Vβ†’W is a diffeomorphism; and that its inverse is the map F(x)=(xβ€²,f(x)).

    • Let’s define f~=fβ—¦G. Show that f~(x)=xn.

    (This exercise will be used, together with [1GB], to address constrained problems, in Section [2D5]).

    Solution 1

    [1H2]

Download PDF
Managing blob in: Multiple languages
This content is available in: Italian English