The derivation of the one-dimensional EulerLagrange equation is one of the classic proofs in mathematics.It relies on the fundamental lemma of calculus of variations. Taking any $\varphi$ that's equal to $(x-x_0)$ near $x_0$ yields $f(x_0)=0$, and so the solution is of the exact same form. Derivation of the one-dimensional EulerLagrange equation.
However, any compactly supported function would have all of its derivatives be $0$ outside its support, which means $\varphi''(x_0)=0$ and so : I am very pleased if I could get a some proof about this theorem. Since f is contineous for a small > 0 there exists a neighborhood V with f ( x) > 0 for. Using 2D and 3D graphics, the book offers new insights into fundamental elements. The problem is: f is a contineous function in R n and we assume that for x 0 f holds f ( x 0) 0. All topics throughout the book are treated with zero. It is about the existence and uniqueness of the solutions 'in the large' of an equation of the form y F(x, y,y) y F ( x, y, y ). I was studying the 'Fundamental lemma of calculus of variations' and I have fully understood the proof to it except for one little step. About proof of fundamental lemma of calculus of variation.
Weakening the Fundamental Lemma of Calculus of Variations.
The fundamental lemma of the calculus of variations can still be applied as long as the equation is true for all smooth functions $\varphi$ that are compactly supported on $(-\infty,x_0)$. This theorem is on the page 16 in the book that I mentioned above. I have a question on a variation of the fundamental lemma.
0 kommentar(er)
