fundamental lemma of calculus of variations
The idea in the calculus of variations is to study stationary points of functionals. To derive a differential equation for such stationary points, the following theorem is needed, and hence named thereafter. It is also used in distribution theory to recover traditional calculus from distributional calculus.
By linearity of the integral, it is easy to see that one only needs to prove the claim for real . If is continuous, this can be seen by purely geometrical arguments. A full proof based on the Lebesgue differentiation theorem is given in . Another proof is given in .
|Title||fundamental lemma of calculus of variations|
|Date of creation||2013-03-22 15:02:04|
|Last modified on||2013-03-22 15:02:04|
|Last modified by||matte (1858)|
|Synonym||fundamental theorem of the calculus of variations|