Article Contents
Article Contents

# The validity of the Euler-Lagrange equation

• We prove the validity of the Euler-Lagrange equationfor a solution $u$ to the problem of minimizing $\int_{\Omega}L(x,u(x),\nabla u(x))dx$,where $L$ is a Carathéodory function, convex in its last variable,without assuming differentiability with respect to this variable.
Mathematics Subject Classification: Primary: 49K20.

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