On generalized derivations and minimum problem of Quadratik Sobolev spaces

In this study, the calculus of variations in the multivariate function extremum problem taken, this is due to the partial derivative of the functional Euler equations become partial differential equations. Such generalized solution of partial differential equations are given difinitions were followed and construction methods. Discussed the meaning of partial differential equations and eaminated generalized definition. Then the quadraic fonctional minimum problems were discussed. Puankare-Friedrichs inequality is used to prove the existence of which we will consider the minimum quadratic functional. This ekstremum problem is shown as generalized solution for limit value problem of Euler-Ostragnaski equation which is one of the extrameller's partial derivative differential equation.