derivation of Euler-Lagrange differential equation (advanced)
Suppose that . Choose such that the closed ball of radius about is contained in . Let be any function whose support lies in this closed ball.
By the definition of ,
By the condition imposed on , the derivative of the second integral is zero. Since the integrand of the first integral and its first derivatives are continuous and the closed ball is compact, the integrand and its first derivatives are uniformly continuous, so it is permissible to interchange differentiation and integration. Hence,
|Title||derivation of Euler-Lagrange differential equation (advanced)|
|Date of creation||2013-03-22 14:45:13|
|Last modified on||2013-03-22 14:45:13|
|Last modified by||rspuzio (6075)|